Question

True or false??

This is a convergent geometric series

Answer 1

i think its convergent, because you can put the argument of the sum like (-3/5)^(i+1) over -5

Answer 2

It is convergent. It's common ratio is -3/5, the absolute value of which is smaller than one. So it does converge.

Answer 3

so true?

Answer 4

yes

Answer 5

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)!