Find the SUm of the infinite series.

I'll do problem 13 to get you started.

The expression is the same as

Then we can do a bit of algebra like so to change that n into n-1

This is so we can get the expression in a(r)^(n-1) form

Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).

We'll plug those a and r values into the infinite geometric sum formula below

S = a/(1-r)

S = (8/7)/(1 - 2/7)

S = (8/7)/(5/7)

S = (8/7)*(7/5)

S = 8/5

S = 1.6

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Answer in fraction form = 8/5

Answer in decimal form = 1.6

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step-by-step explanation: