Question

Find the sum of the series

-9+(-9/5)+(-9/25)+...+(-9/5^(n-1))+...

Answer 1

Do you know how wolfram got that? My professor cares more about the work then the bottom line.

Answer 2

\[-9\times (1+\frac{1}{5}+\frac{1}{5^2}+...\]
\[=-9\times \frac{1}{1-\frac{1}{5}}=-9\frac{1}{\frac{4}{5}}=-9\frac{5}{4}=-\frac{45}{4}\]

Answer 3

use
\[a+ar+ar^2+ar^3+...=\frac{a}{1-r}\] if \(0<r<1\)