You are here:

Calculus/sum of infinite series

Advertisement

Expert: Alon Mandes - 11/21/2008


Question
i need to find the sum of the series (2+(-1/3)^n)/2^n from n=0 to inf. i really have no idea how to do these kind of problems any help is greatly appreciated. thanks
drae

Answer
∞
∑ { [2+(-1/3)^2]/2^n } =
n=0

∞
∑ { 2/2^n+(-1)^n/6^n } =
n=0

 ∞                ∞
2 ∑ { (1/2)^n } + ∑ { (-1)^n/6^n } =
 n=0             n=0

=2/(1-1/2) + 1 - 1/6 + 1/36 -1/216 + 1/1296 - 1/7776 + 1/46656 - 1/279936 +..

=4 + 1 - 1/6 + 1/36 -1/216 + 1/1296 - 1/7776 + 1/46656 - 1/279936 +..

=4 + 1/(1-36) - (1/216)*[1+1/36+1/1296+....

=4 + 36/35 - (1/216)*[1/1-36]

=4 + (36/35) - (1/216)*(36/35)

=4 + (36/35)(1-1/216)

=4 + (36/35)(215/216)

5.02.

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.