Series of Sequences

Question

I was given this summation problem and I thought that it would converge to 9/11, but got the question wrong. Are you able to show how to solve this problem? Thanks!

Answer 1

Try separating into two separate fractions: (1/11)ⁿ + (9/11)ⁿ, then realize each of these is an infinite geometric series with |r| < 1, so each converges.

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