Question

∑[i=1,∞,(12)(0.25)^i]

Answer 1

\[12\sum_{i=1}^{\infty}\left(\frac{1}{4}\right)^i\] is a start

Answer 2

you are starting at \(i=1\) not \(i=0\) right?

Answer 3

correct. & i am to find the sum of this infinite geometric series.

Answer 4

correct. & i am to find the sum of this infinite geometric series.

Answer 5

\[\sum_{i=1}^{\infty}r^i=\frac{r}{1-r}\] so
\[\sum_{i=1}^{\infty}(\frac{1}{4})i=\frac{\frac{1}{4}}{1-\frac{1}{4}}\]
\[=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}\]
and
\[12\times\frac{1}{3}=4\]

Answer 6

Thank you SO much.

Answer 7

yw