Question

Identify whether the series summation of 15 open parentheses 4 close parentheses to the I minus 1 power from 1 to infinity is a convergent or divergent geometric series and find the sum, if possible.

Answer 1

\[15\sum_{k=1}^{\infty}4^{-k}\]?

Answer 2

like that?

Answer 3

well
\[\sum_{k=0}^{\infty}\frac{1}{4^k}=\frac{1}{1-\frac{1}{4}}=\frac{4}{3}\] so this would in fact converge. then multiply by 15

Answer 4

i always have to think "do you start at one or at zero" seems like i could remember...

Answer 5

wouldn't 4 ^(-infinity) converge to 0?