Find the sum of the convergent series. sum_{n=0}^infty5(frac23)^n

Khadija Wells

Khadija Wells

Answered question

2021-02-15

Find the sum of the convergent series.
n=05(23)n

Answer & Explanation

toroztatG

toroztatG

Skilled2021-02-16Added 98 answers

To find the sum of the convergent series: n=05(23)n
Solution:
Expanding the given series, we get
n=05(23)n=5(23)1+5(23)2+5(23)3+...
=5[(23)1+(23)2+(23)3+...]
Now, taking the series (23)1+(23)2+(23)3+...
Here,we can find that sequence is in geometric progression.
First term is a1=23
Common ratio is:
r=(23)2(23)
=23
Sum of infinite terms of G.P. is given as:
S=a11r
Sum of the sequence (23)1+(23)2+(23)3+... will be:
S=23123
=2313
=2
Now, sum of the series n=05(23)n will be:
n=05(23)n=5[(23)1+(23)2+(23)3+...]
=52
=10
Hence, required sum is 10.
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?