Question

\[\sum_{k=1}^{\infty} 1/5^k\] How do I turn that into a function of Sn? I can't seem to figure it out.

Answer 1

I know that the answer is Sn=(5^n-1)/(4*5^n) but I'm not sure how that happens.

Answer 2

\[\sum_{k=1}^{\infty} \frac{1}{5^k} = \frac{1}{5} + \frac{1}{25} + \frac{1}{125} +...\]As you can see it is a geometric series, you can find Sn using the formula for geometric series

Answer 3

I see, I was getting the answer at 5/4 when the answer was really 1/4 since the geometric series starts at 0 normally and this starts at 1, so all I had to do was subtract 1 from the final answer.