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

Wribreeminsl 2021-01-19 Answered
Find the sum of the series:
n=0((52n)(13n))
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Expert Answer

yunitsiL
Answered 2021-01-20 Author has 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
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