Determine the sum of the following series. \sum_{n=1}^\infty (\frac{1^n+9^n}{11^n})

philosphy111of

philosphy111of

Answered question

2021-11-13

Determine the sum of the following series.
n=1(1n+9n11n)

Answer & Explanation

Jennifer Hill

Jennifer Hill

Beginner2021-11-14Added 10 answers

We have to find sum of series.
Series is given as:
n=1(1n+9n11n)
We will use geometric series test to find sum of series .
Geometric series test is given below:
n=1arn1
if |r|<1 (series converges)
=a1r (infinite gp)
With the help of geometric series we will find sum .
Work is shown below:
n=1(1n+9n11n)
n=1(111)n+(911)n
n=1(111)n=1111111
n=1(111)n=110
n=1(911)n=9111911
n=1(911)n=92
n=1(111)n+(911)n=110+92
n=1(111)n+(911)n=235

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