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estebananaya
 2 years ago
Best ResponseYou've already chosen the best response.0i think its convergent, because you can put the argument of the sum like (3/5)^(i+1) over 5

Lumenaire
 2 years ago
Best ResponseYou've already chosen the best response.0It is convergent. It's common ratio is 3/5, the absolute value of which is smaller than one. So it does converge.

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0Rewrite 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)!
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