Question

what does the following geometric series converge to...
10+5+2.5+1.25+...+10+5+2.5+1.25+...

Answer 1

\[\sum_{i=1}^{\infty}10(\frac{1}{2})^{i-1}=\frac{10}{1-(\frac{1}{2})}=20\]

Answer 2

We know this series converges because \[\left| r \right|<1\]where \[r=\frac{1}{2}\]for this series

Answer 3

Thanks! I understand