Determine whether the series converges or diverges and justify your answer. If the series converges, find its sum sum_{n=0}^inftyfrac{3^{n-2}}{4^{n+1}}

permaneceerc

permaneceerc

Answered question

2020-12-25

Determine whether the series converges or diverges and justify your answer. If the series converges, find its sum
n=03n24n+1

Answer & Explanation

Usamah Prosser

Usamah Prosser

Skilled2020-12-26Added 86 answers

We have given a series,
n=03n24n+1
Let,
an=3n24n+1
an+1=3n+124n+1+1
an+1=3n14n+2
By the ratio test we know that,
n=0an+1an=L
If L<1 then series converges, if L>1 then it diverges
So now we have,
an+1an=3n14n+23n24n+1
an+1an=3n14n+24n+13n2
an+1an=3n314n424n43n32
an+1an=14131
an+1an=34
n=0an+1an=34
Hence, the series converges.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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