Find the sum of the series: sum_{n=0}^infty((frac{5}{2^n})-(frac{1}{3^n}))

Wribreeminsl

Wribreeminsl

Answered question

2021-01-19

Find the sum of the series:
n=0((52n)(13n))

Answer & Explanation

yunitsiL

yunitsiL

Skilled2021-01-20Added 108 answers

The given series is
n=0((52n)(13n))
Rewrite the given series as shown below:
n=0((52n)(13n))=n=0(52n)n=0(13n)
From above it can be observed that given series is the sum of two geometric series. Hence, the sum of series is obtained as,
n=0((52n)(13n))=n=0(52n)n=0(13n)
=5n=0(12n)n=0(13n)
=5(12112)(13113)
=5(1212)(1323)
=5(1)(12)
=92

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?