Question

Is this convergent or divergent and find the sum if possible

Answer 1

The given series is

`250+200+160+128+\cdots`

Notice that the series is a geometric series with common ratio as:

`r=(4)/(5)`

The sum to infinity is:

`S_(\infty)=(a)/(1-r)`

Notice that the first term is a=250

Hence the sum to infinity is

`\begin{gathered} S_(\infty)=(250)/(1-(4)/(5)) \\ S_(\infty)=1250 \end{gathered}`

Therefore the sum is 1250

Hence the it converges