Find the sum of the convergent series. sum_{n=1}^inftyfrac{4}{n(n+2)}

Daniaal Sanchez

Daniaal Sanchez

Answered question

2020-11-08

Find the sum of the convergent series.
n=14n(n+2)

Answer & Explanation

Velsenw

Velsenw

Skilled2020-11-09Added 91 answers

Given series,
n=14n(n+2)
The series can be written as n=14n(n+2)
=n=1(2n2n+2)
=(223)+(112)+(2325)+(1213)+(2527)+...
=2+1
=3
Therefore,
The sum of the convergent series is
n=14n(n+2)=3
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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