generals336
2020-10-25
Answered

Determine whether the given series is convergent or divergent. Explain your answer. If the series is convergent, find its sum.

$\sum _{n=0}^{\mathrm{\infty}}\frac{{3}^{n}+{2}^{n+1}}{{4}^{n}}$

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Mayme

Answered 2020-10-26
Author has **103** answers

Given the series:

Rewriting the given series as sum of two series:

Hence we get sum of two geometric series:

Since both

Both the individual geometric series converge.

The given series is sum of two converging, hence the given series

The sum of an infinite geometric series is given as:

The sum of the series will be:

The sum of the given series will be:

Final Answer:

The given series is converging.

The sum of series is 8

Jeffrey Jordon

Answered 2021-12-17
Author has **2262** answers

Answer is given below (on video)

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