Use the formula for the sum of a geometric series to find the sum, or state that the series diverges. sum_{n=2}^inftyfrac{7cdot(-3)^n}{5^n}

he298c 2021-01-31 Answered
Use the formula for the sum of a geometric series to find the sum, or state that the series diverges.
n=27(3)n5n
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wornoutwomanC
Answered 2021-02-01 Author has 81 answers

Given that:
The series is n=27(3)n5n
By using,
Geometric series test :
A geometric series n=0a1rn or n=1a1rn1 is converges if and only if - 1 < r < 1 and its sum is,
n=1a1rn1=a11r
Consider the series,
n=27(3)n5n=7n=2(3)n5n
=7n=2(35)n
The series n=2(35)n is the geometric series with first term (a1) is 925 and common ratio (r)=35
Also, |r|=|35|1
Then,
By the geometric series,
The series n=2(35)n is converges and its sum,
n=2(35)n=9251(35)=9(5)25(8)=940
Then,
n=27(3)n5n=7n=2(35)n=7(940)=6340
Therefore,
The series n=27(3)n5n is converges and its sum is 6340

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Jeffrey Jordon
Answered 2021-12-27 Author has 2313 answers

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