Write out the first few terms of the series sum_{n=0}^inftyfrac{(-1)^n}{5^n} What is the​ series' sum?

avissidep

avissidep

Answered question

2021-02-21

Write out the first few terms of the series
n=0(1)n5n
What is the​ series' sum?

Answer & Explanation

Velsenw

Velsenw

Skilled2021-02-22Added 91 answers

Consider the series
n=0(1)n5n
n=0(1)n5n=(1)050+(1)151+(1)252+(1)353+...
n=0(1)n5n=11+15+152+153+...
n=0(1)n5n=115+152153+...
Series sum
n=0(1)n5n=115+152153+...
It is a infinite geometric series with first term a=1 and common ratio r=15
Sum of a infinite geometric series is given by
S=a1r
S=11(15)
S=11+15
S=15+15
S=56
First term is =1
Sum =56
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?