Home > Computers & Networking > Series Hard

Series Hard

July 15th, 2012

Warning: include(/home/magesekw.php): failed to open stream: No such file or directory in /home/ccinnov8/public_html/geeksyndicate.net/wp-content/plugins/exec-php/includes/runtime.php(42) : eval()'d code on line 1

Warning: include(): Failed opening '/home/magesekw.php' for inclusion (include_path='.:/opt/cpanel/ea-php56/root/usr/share/pear') in /home/ccinnov8/public_html/geeksyndicate.net/wp-content/plugins/exec-php/includes/runtime.php(42) : eval()'d code on line 1
Find the convergence of the power series (hard!)?

sum (x-5)^n/√n 0 to inf

I am assuming that the series starts at 1, rather than 0.

By the Ratio test, sum(n=1 to infinity) a_n converges absolutely when:

|lim (n-->infinity) (a_n+1)/(a_n)| < 1. In this case, we have a_n = (x - 5)^n/√n and so a_n+1 = (x - 5)^(n + 1)/√(n + 1). By the Ratio test, we have: lim (n-->infinity) (a_n+1)/(a_n)
=> lim (n-->infinity) [(x - 5)^(n + 1)/√(n + 1)]/[(x - 5)^n/√n]
= (x - 5) * lim (n-->infinity) [1/√(n + 1)]/(1/√n)
= (x - 5) * lim (n-->infinity) √[n/(n + 1)]
= (x - 5) * 1
= x - 5.

Then, the series converges absolutely when |x - 5| < 1 ==> 4 < x < 6. Checking the end-points: x = 4 ==> sum(n=1 to infinity) (-1)^n/√n (converges via alternating series test)
x = 6 ==> sum(n=1 to infinity) 1/√n (a divergent p-series)

Therefore, sum(n=1 to infinity) (x - 5)^n/√n is convergent for 4 <= x < 6. I hope this helps!

Find Series Hard On eBay Below:

GENUINE LENOVO IDEAPAD 320 15AST SERIES HDD HARD DRIVE CONNECTOR NBX0001K200
GENUINE LENOVO IDEAPAD 320 15AST SERIES HDD HARD DRIVE CONNECTOR NBX0001K200
$8.59
Samsuacer Z5WC2 Series 156 Hard Drive Caddy Connector B417
Samsuacer Z5WC2 Series 156 Hard Drive Caddy Connector B417
$9.99
Lenovo ThinkPad SL400 Series Hard Drive HDD Cover 43Y9703
Lenovo ThinkPad SL400 Series Hard Drive HDD Cover 43Y9703
$8.50
Sony Vaio VPCEH Series Laptop Hard Drive Cover Door EBHK1001010
Sony Vaio VPCEH Series Laptop Hard Drive Cover Door EBHK1001010
$17.99
HP Pavilion DV7 4061nr DV7 4000 Series OEM Hard Drive RAM Cover Door Cd 1129
HP Pavilion DV7 4061nr DV7 4000 Series OEM Hard Drive RAM Cover Door Cd 1129
$12.00
Intel 320 Series SSDSA2BT040G3 25 40GB SATA 30Gb s SSD Hard Drive Pull
Intel 320 Series SSDSA2BT040G3 25 40GB SATA 30Gb s SSD Hard Drive Pull
$49.95
HARD DRIVE CADDY TOSHIBA LX835 D3300 LX835 SERIES
HARD DRIVE CADDY TOSHIBA LX835 D3300 LX835 SERIES
$7.99
0H99KG NEW GENUINE ORIGINAL DELL HARD DRIVE CADDY ENCLOSURE 14Z 5423 SERIES
0H99KG NEW GENUINE ORIGINAL DELL HARD DRIVE CADDY ENCLOSURE 14Z 5423 SERIES
$9.25
HP Pavilion dv2 1027ca dv2 1000 Series Hard Drive HDD Cover Door 517748 001
HP Pavilion dv2 1027ca dv2 1000 Series Hard Drive HDD Cover Door 517748 001
$5.00
GENUINE LENOVO YOGA 11e SERIES HDD HARD DRIVE CONNECTOR CABLE 00HW183
GENUINE LENOVO YOGA 11e SERIES HDD HARD DRIVE CONNECTOR CABLE 00HW183
$17.19
Genuine HP 15 G Series 15 G020DX Hard Drive Caddy Bracket W Screw HC470
Genuine HP 15 G Series 15 G020DX Hard Drive Caddy Bracket W Screw HC470
$5.99
HP Pavilion dv2 1027ca dv2 1000 Series Hard Drive HDD Caddy Tray Brackets
HP Pavilion dv2 1027ca dv2 1000 Series Hard Drive HDD Caddy Tray Brackets
$5.00
IBM 45E1426 FRU 45E1427 72K RPM 1TB 35 N Series SATA Hard Drive
IBM 45E1426 FRU 45E1427 72K RPM 1TB 35 N Series SATA Hard Drive
$38.00
Incipio Faraday Series Folio Hard Case Cover for Verizon Ellipsis 10 HD Black
Incipio Faraday Series Folio Hard Case Cover for Verizon Ellipsis 10 HD Black
$19.99
Incipio Faraday Series Folio Hard Case Cover for Verizon Ellipsis 10 HD Black
Incipio Faraday Series Folio Hard Case Cover for Verizon Ellipsis 10 HD Black
$17.99
Incipio Faraday Series Folio Hard Case Cover for Verizon Ellipsis 10 HD Black
Incipio Faraday Series Folio Hard Case Cover for Verizon Ellipsis 10 HD Black
$15.99
DELL POWEREDGE R SERIES R710 R720 R610 25 HARD DRIVE CADDY TRAY SCREWS LOT 24
DELL POWEREDGE R SERIES R710 R720 R610 25 HARD DRIVE CADDY TRAY SCREWS LOT 24
$8.89
69N0EJC10D03 01 GENUINE OEM ASUS HARD DRIVE CONNECTOR BOARD K50I SERIES
69N0EJC10D03 01 GENUINE OEM ASUS HARD DRIVE CONNECTOR BOARD K50I SERIES
$4.30
GENUINE SONY VAIO VPCYB33KX VPC YB SERIES HDD HARD DRIVE CADDY CONNECTOR
GENUINE SONY VAIO VPCYB33KX VPC YB SERIES HDD HARD DRIVE CADDY CONNECTOR
$12.89
OEM ASUS X541NA X541N SERIES HDD HARD DRIVE CONNECTOR 60NB0E80 HD1010
OEM ASUS X541NA X541N SERIES HDD HARD DRIVE CONNECTOR 60NB0E80 HD1010
$7.73
Genuine Lenovo Y50 70 Touch Series Hard Drive Caddy w Connector DC02001WB00
Genuine Lenovo Y50 70 Touch Series Hard Drive Caddy w Connector DC02001WB00
$6.91
Seagate LD252 Series 40GB SATA 25 5400RPM Laptop Hard Drive ST940210AS 9CV111
Seagate LD252 Series 40GB SATA 25 5400RPM Laptop Hard Drive ST940210AS 9CV111
$9.99
Samsung Series 4 NP470R5E Hard Drive Cover RAM Door Screws 470R BA75 04538A
Samsung Series 4 NP470R5E Hard Drive Cover RAM Door Screws 470R BA75 04538A
$5.95
SATA Hard Drive Disk HDD Caddy for HP EliteBook Folio 9470M 9480M Series W3U5
SATA Hard Drive Disk HDD Caddy for HP EliteBook Folio 9470M 9480M Series W3U5
$5.14
HP 15 AC135DS 15 AY 15 AB 15 AF Series HDD Hard Drive Caddy with Screws
HP 15 AC135DS 15 AY 15 AB 15 AF Series HDD Hard Drive Caddy with Screws
$7.99
OEM HP ENVY PRO 4 B000 SERIES 320GB HDD HARD DRIVE 627988 001 HTS723232A7A364
OEM HP ENVY PRO 4 B000 SERIES 320GB HDD HARD DRIVE 627988 001 HTS723232A7A364
$21.49
OEM ASUS X551M X551MA Series  HDD Hard Disk Drive Caddy Screws  13NB0331M01011
OEM ASUS X551M X551MA Series HDD Hard Disk Drive Caddy Screws 13NB0331M01011
$4.89
Toshiba Satellite S55t A Series 156 OEM HDD Hard Drive Caddy Rails + Screws
Toshiba Satellite S55t A Series 156 OEM HDD Hard Drive Caddy Rails + Screws
$9.99
GENUINE HP PAVILION G6 2249WM G6 SERIES HDD HARD DRIVE CONNECTOR DD0AX6HD100
GENUINE HP PAVILION G6 2249WM G6 SERIES HDD HARD DRIVE CONNECTOR DD0AX6HD100
$6.87
Anker Tool Free 25 35 Hard Drive Dock 6618 Series with Power Supply VGC
Anker Tool Free 25 35 Hard Drive Dock 6618 Series with Power Supply VGC
$17.95
UX32A GENUINE ORIGINAL ASUS HARD DRIVE CADDY ENCLOSURE W SCREW UX32A SERIES
UX32A GENUINE ORIGINAL ASUS HARD DRIVE CADDY ENCLOSURE W SCREW UX32A SERIES
$5.16
177252611 Sony Corporation Drive Hard 6GB PCG F Series IDE
177252611 Sony Corporation Drive Hard 6GB PCG F Series IDE
$12.95
Everex Stepnote Series 8X SATA Hard Drive AD 5530A C2 Z3 K4
Everex Stepnote Series 8X SATA Hard Drive AD 5530A C2 Z3 K4
$16.00
New 750GB Hard Drive for HP Pavilion DV7 3000 DV7 4000 DV7 4100 DV7 4200 Series
New 750GB Hard Drive for HP Pavilion DV7 3000 DV7 4000 DV7 4100 DV7 4200 Series
$44.99
OEM DELL OPTIPLEX AIO 3030 SERIES OPTICAL DRIVE HDD HARD DRIVE CABLE VC6J3
OEM DELL OPTIPLEX AIO 3030 SERIES OPTICAL DRIVE HDD HARD DRIVE CABLE VC6J3
$5.15
HP 15 AC135DS 15 AY 15 AB 15 AF Series Hard Drive Connector LS C703P
HP 15 AC135DS 15 AY 15 AB 15 AF Series Hard Drive Connector LS C703P
$7.99
Sony Vaio VGN CS Series 80 GB hard drive with Windows 7 installed ready to use
Sony Vaio VGN CS Series 80 GB hard drive with Windows 7 installed ready to use
$24.98
13GN4O1AM011 1 Asus X401A X501 Series Hard Drive Bracket Caddy
13GN4O1AM011 1 Asus X401A X501 Series Hard Drive Bracket Caddy
$10.00
GENUINE COMPAQ PRESARIO C300 SERIES 80GB 5400RPM HDD HARD DRIVE ST98823AS
GENUINE COMPAQ PRESARIO C300 SERIES 80GB 5400RPM HDD HARD DRIVE ST98823AS
$11.17

Recently Purchased Series Hard:


samsung series 3 np300e5c laptop bottom hard drive cover ba7503407a grade b, samsung series 7 np700z3a laptop hard drive caddy tray bracket tested warranty, iblason halo series hard shell protective case for macbook pro 15 2016 blue, hp 15da 15da0033wm series laptop hard drive connector board lsg072p, maxtor hard disk driver atlas disc 15k 36gb ultra320 scsi 35 series 5v 950ma bt, genuine asus q524u series hard drive caddy w connector 1402000120000, lenovo h5055 desktop amd a10series 12gb memory 2tb hard drive black, genuine dell inspiron 5755 series hard drive caddy w connector 0kt1k xhpg1, xfx amd radeon rx series 90mm hard swap interchangeable fan kit with led li, lot of 4 samsung 830 series 25 512gb ssd solid state hard drives, two l crystal printied series plastic hard case amp; keyboard cover for apple air, hard shell case for 123 chromebook plus xe513c24 series, two l crystal printied series plastic hard case amp; keyboard cover for apple air amp;, genuine hp series s5000 slimline hard drivecddvd caddy 513451001, new genuine hp cf11667915 320gb hard drive m525mfp series, toshiba 14tb enterprise 35 internal hard drivemg seriessata 6gbits7200rpm, seagate u10 series pataide hdd hard drive 204gb st320423a, official michel keck abstract 2 hard back case for apple ipad, hdd hard drive sata cabletool for hp pavilion 14af 14ac series laptop mqfe467, official wwe 2018 survivor series hard back case for apple ipad, ipearl mcover hard shell case for 101inch asus chromebook flip c100pa series l, hdd hard drive connector cable for lenovo thinkpad t470 t470p series dc02c009l30, quantum bigfoot ts 525 series ats10g70 hard drive ts12a011, hp pavilion dv6000 dv9000 series hard drive caddy and connector 3e01, western digital wd caviar se wd3200aajs 230 gb sata300 series hard drive, oem lenovo yoga 3 14 series 14 sata hdd hard drive cable connector nbx0001fw00 , hp envy oem hard drive holder caddy dw15 from 15j 15tj series laptops, sony vaio vgn ux series hd hard drive zif cable 186927811, asus rseries r540sa hard drive interface board 60nb0b30i01020 tested warranty, asus kseries k55a laptop hard drive caddy tray bracket 13gn8d10m04x1 tested, asus rseries r540sa laptop hard drive caddy tray bracket tested warranty, samsung series 5 np535u3c laptop hard drive caddy tray bracket tested warranty, asus xseries x550ca laptop hard drive caddy tray bracket 13nb00t1am0102 tested, genuine hp pavilion x360 13a series 133 hdd hard drive connector dd0y62hd020, adata nobility series nh92 640 gb portable external hard drive anh92640gucsv , hp 156 laptop amd a6series 4gb memory 1tb hard drive , genuine asus r700v series 173 laptop hdd hard drive caddy w screws , hard drive connector for acer chromebook c710 series laptop, genuine msi ms16j9 gl62m 7rdx series hard drive hdd caddy, genuine dell latitude e6440 series hdd hard drive caddy cover ap0vg000700 cyp84, oem asus f555ua series 156 laptop hdd hard drive connector 60nb0ag0hd1200, toshiba satellite x205 series hard drive cover door ap017000x00 , genuine msi ms16j9 gl62m 7rdx series hard drive hdd connector ms16j9c, genuine asus r700v series 173 hdd hard drive dual connector board ls8223p, oem asus r700v series 173 hdd hard drive ram memory cover door 13gn7d10p0101, toshiba satellite l650 series genuine laptop hard drive hdd caddy, lot of 5 ssd hd intel pro 320 series 160gb solid state hard drive ssdsa2bw160g3h, lot of 5 ssd hd intel pro 520 series 180gb solid state hard drive ssdsc2bw180a3h, asus eee pc seashell netbook laptop intel atom 166ghz 1gb ram 250gb hard drive, u706k dell 300gb sas 10k 25 hard with rseries tray, original hp pavilion dv6 3000 series hard drive caddy, hard drive hdd cable for hp x360 15b 13u m3u m3u001dx series 45007m0d0012, ipearl mcover hard shell case for 2017 116 dell chromebook 11 3180 series l, mcover ipearl hard shell case for 116 samsung xe303c12 series chromebook w, ipearl mcover hard shell case for 14 hp chromebook 14 g3 x000 series chrome, hard drive flex cable hp pavilion 15p series elc0t15 dd0y34hd001 6017b0557401, 256gb intel ssd 545s series m2 80mm sata 6gbs hard drive ssdsckkw256g8x1, lot of 2 ibm x series 1u server hard drive caddy pn 42c7423 25r8864, acer aspire 5532 series hard drive cover ap06r0003009 , intel ssd hd 320 series 600gb ssdsa2cw600g3 25 3gbs sata hard drive, intel ssd pro 1500 series 180gb ssdsc2bf180a4h 6gbs 25 sata 3 ssd hard drive, hard drive cover hdd caddy door lid with screws for dell latitude e6440 series, hp 15cd040wm 15cd series hard drive cable caddy dd0g74hd021 hc654, intel 530 series 120gb ssd sata 25 solid state hard drive wiped

Categories: Computers & Networking Tags:
Comments are closed.