Consider the series below: infinity "series symbol" n= 1 ((1+5^n)/(27^n)) determine whether or not the series converges. If it converges, find the sum.

Note:
I don't know how to solve or work out so show all your work. And give the answer in EXACT FORM example 3pi, sqrt(2), ln(2) not decimal approximations like 9.424,1.4242,1232

1 answer

Break it into two sums.
∑1/27^n + ∑(5/27)^n
both of these are just geometric series, which you know how to sum.
The result is 38/143
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