Question

What is the sum of the series sum from n equals 1 to infinity of negative 4 times five eighths to the n power question mark

negative five halves
twenty thirds
negative twenty thirds
twenty thirteenths

Answer 1

\[\sum_{n=1}^{n=\infty}-4(\frac{ 5 }{8 })^{n}\](please double check to make sure I interpreted the series formula correctly)
for the sum of an infinite geometric series:
\[S_{n}=\frac{ a_{1} }{ (1-r) }\]
where a1 is the first term and r is the common ratio. to find a1, plug in n = 1 into the series formula and calculate the first term. for the common ratio r, notice in the series formula, each time n increases by 1, it multiplies the previous term by (5/8) so r = 5/8.

Answer 2

It was negative twenty thirds