Question

how to solve the geometric series

Answer 1

\[\sum_{k=0}^{\infty} \left( \frac{ 1 }{ 3 } \right)^{k} (5^{3-k})\]

Answer 2

can someone show me how to solve the series the answer is \[\frac{ 2500 }{ 19 }\]

Answer 3

honestly, I don't get 2500/19
maybe there is someone who can help you

Answer 4

\[5^3,\frac{5^2}{3},\frac{5}{3^2},......\]Here \(\frac{1}{15}\) is common ratio so \[s_{\infty}=\frac{a}{(1-r)}\]

Answer 5

\[a=5^3\]\[s_{\infty }=\frac{5^3}{(1-\frac{1}{15})}\]

Answer 6

As Jitesh said, you can find the sum of geometric series like that.
Anyway, the answer wouldn't be 2500/19 after you calculate it. Is 2500/19 really the true answer?