Power Series

Dell D Series Dock Port Replicator 90W Power Adapter
Dell D Series Dock Port Replicator 90W Power Adapter
Paypal   US $35.99
Monster Cable AVS2000 Power Signature Series AVS 2000
Monster Cable AVS2000 Power Signature Series AVS 2000
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Power Rangers Dino Thunder Complete Series
Power Rangers Dino Thunder Complete Series
Paypal   US $11.00
HP DeskJet 930C Series Printer cable power cord 12784
HP DeskJet 930C Series Printer cable power cord 12784
Paypal   US $18.99
Power Rangers Zeo Complete Series
Power Rangers Zeo Complete Series
Paypal   US $43.00
Power Rangers SPD Complete Series
Power Rangers SPD Complete Series
Paypal   US $30.00
Power Rangers Operation Overdrive Complete Series
Power Rangers Operation Overdrive Complete Series
Paypal   US $20.50
Power Rangers Mystic Force Complete Series
Power Rangers Mystic Force Complete Series
Paypal   US $14.50
Cooler Master eXtreme Power Plus Series 500W ATX12V V2
Cooler Master eXtreme Power Plus Series 500W ATX12V V2
Paypal   US $11.50
Power Rangers Ninja Storm Complete Series
Power Rangers Ninja Storm Complete Series
Paypal   US $14.62
Power Rangers RPM Complete Series
Power Rangers RPM Complete Series
Paypal   US $41.00
Power Rangers Turbo Complete Series
Power Rangers Turbo Complete Series
Paypal   US $9.95
4 Bottles Power Boost Pro Series Solar Panel Cleaner
4 Bottles Power Boost Pro Series Solar Panel Cleaner
Paypal   US $49.95
Condor Pac Series Autoswitching DC Power Supply
Condor Pac Series Autoswitching DC Power Supply
Paypal   US $15.75
T112 Dell Optiplex DA 2 SERIES Power Adapter
T112 Dell Optiplex DA 2 SERIES Power Adapter
Paypal   US $9.99
Cutler Hammer Power Series Panelmate
Cutler Hammer Power Series Panelmate
Paypal   US $59.95
1994 POWER RANGERS NEW SEASON TRADING CARDS BOTH SERIES
1994 POWER RANGERS NEW SEASON TRADING CARDS BOTH SERIES
Paypal   US $17.99
Power Macintosh 6100 Series 7100 Series 8100 Series
Power Macintosh 6100 Series 7100 Series 8100 Series
Paypal   US $.99
Compaq Series PS4000 Power Supply PN 270236 002
Compaq Series PS4000 Power Supply PN 270236 002
Paypal   US $.99
Power Supply 195V 3A 4 sony SONY VAIO PCG 700 SERIES
Power Supply 195V 3A 4 sony SONY VAIO PCG 700 SERIES
Paypal   US $11.48
Rockford Fosgate Power T5002 1000w rms ELITE SERIES
Rockford Fosgate Power T5002 1000w rms ELITE SERIES
Paypal   US $165.00
4 X 5MM LONG SERIES HSS DRILL BITS DIY power tool
4 X 5MM LONG SERIES HSS DRILL BITS DIY power tool
Paypal   US $1.53
10 X 3MM LONG SERIES HSS DRILL BITS DIY power tool
10 X 3MM LONG SERIES HSS DRILL BITS DIY power tool
Paypal   US $1.53
Power Color GameFX Board Series
Power Color GameFX Board Series
Paypal   US $1.00
Day Tripper GPS Power Bundle Power Series
Day Tripper GPS Power Bundle Power Series
Paypal   US $6.99
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iRobot 560 Roomba Vacuuming Robot, Black and Silver iRobot 560 Roomba Vacuuming Robot, Black and Silver
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56101 The Roomba 560 features our newest innovations in vacuum performance, room navigation, edge and corner cleaning, advanced anti-tangle technology and transitioning from carpets to hard floors. Includes: -One compact self-charging home base...

Hayward SP1580X15 Power-Flo LX Series 1-1/2-Horsepower Above-Ground Pool Pump with Cord Hayward SP1580X15 Power-Flo LX Series 1-1/2-Horsepower Above-Ground Pool Pump with Cord
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Hayward Economy Above Ground Pump Perfect for most above ground pools, this economical pump by Hayward combines durable, corrosion proof construction with advanced features and performance. Features Self Priming1 1/2 inch intake & discharge, high performance impeller, heat resistant, double sided seal for long motor life and a 6 foot, 120 volt power cord.

Hayward SP1580 Power-Flo LX Series 1-Horsepower Pool Pump with Cord Hayward SP1580 Power-Flo LX Series 1-Horsepower Pool Pump with Cord
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Hayward Economy Above Ground Pump Perfect for most above ground pools, this economical pump by Hayward combines durable, corrosion proof construction with advanced features and performance. Features Self Priming1 1/2 inch intake & discharge, high performance impeller, heat resistant, double sided seal for long motor life and a 6 foot, 120 volt power cord.

Glee: The Complete First Season [Blu-ray] Glee: The Complete First Season [Blu-ray]
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Join the club and bring home the fun with Glee Karaoke and Glee Jukebox— available only on DVD! A talented group of high school misfits transforms into a performing sensation with the help of a dedicated teacher...

Blue's Clues - Blue's Room - Alphabet Power Blue's Clues - Blue's Room - Alphabet Power
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Adventures from the Book of Virtues The Box Set Adventures from the Book of Virtues The Box Set
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Studio: Porchlight Ent Inc Release Date: 08/12/2008

Tinderbox (Program 7) / New Order of Oil (Program 8) (The Prize - The Epic Quest for Oil, Money & Power Tape 4) [VHS] Tinderbox (Program 7) / New Order of Oil (Program 8) (The Prize - The Epic Quest for Oil, Money & Power Tape 4) [VHS]
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Tae-Bo Focus Series - The Power Within [VHS] Tae-Bo Focus Series - The Power Within [VHS]
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Dremel 300-1/24 300 Series Variable-Speed Rotary Tool Kit Dremel 300-1/24 300 Series Variable-Speed Rotary Tool Kit
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Perfect for the do-it-yourselfer or anyone who is new to rotary tools, the Dremel 300-1/24 Variable-Speed Rotary Kit helps you complete a wide range of household, fine art, and repair projects. The rotary tool itself features an updated design for optimum comfort and control, as well as variable-speed control that allows you to set the speed of the tool to match specific accessories or tasks...


Power Series
Power Series?

A fair coin is tossed repeatedly. The probability that the first head occurs on the nth toss is P(n)=(1/2)^n. When this action is repeated many times, the average # of tosses required until the first head is:
E(n)=sum from 1 to inf n*P(n)
This # is called the expected value of n

A) use the power series: 1/1-x = sum from 0 to inf of x^n, for |x|<1 to get a power series representation for f(x)=1/(1-x)^2 and give interval of convergence

B) what is the relation between E(n) and the series found in (a)?

C) what is the expected value of n? Be sure to give specific reason why you can make your conclusion.

I am completely clueless on this. If someone could just help me on each part not exactly answer it that would be very helpful. Thanks

A) 1/(1-x) = Sum(x^n, n=0 to inf) for |x| < 1
Take the derivative of both sides:
1/(1-x)^2 = Sum(n x^(n-1), n = 1 to inf) for |x|<1 [Taking the derviative give the same radius of of convergence.]

B) E(n) = Sum(n(1/2)^n, n=1 to inf) =
(1/2) Sum(n(1/2)^(n-1), n = 1 to inf) =
(1/2)(1/(1-(1/2))^2 [Plug x = 1/2 into summation above]
=(1/2)(1/(1/4)) = (1/2)*(4) = 2
C) The expected number of tosses to get heads is 2.

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