Here's the question you clicked on:
kaykim95
True or false?? This is a convergent geometric series
i think its convergent, because you can put the argument of the sum like (-3/5)^(i+1) over -5
It is convergent. It's common ratio is -3/5, the absolute value of which is smaller than one. So it does converge.
Rewrite it a little:\[\sum_{i=1}^{\infty}\frac{ 3^{i+1} }{ (-5)^{i+2} }=\sum_{i=1}^{\infty}\frac{ 3^{i+1} }{ (-5)(-5)^{i+1} }=-\frac{ 1 }{ 5 }\sum_{i=1}^{\infty}\left( -\frac{ 3 }{ 5 } \right)^{i+1}\]Now read @Lumenaire 's answer (again)!