SOLUTION
The given series is
[tex]250+200+160+128+\cdots[/tex]
Notice that the series is a geometric series with common ratio as:
[tex]r=\frac{4}{5}[/tex]
The sum to infinity is:
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
Notice that the first term is a=250
Hence the sum to infinity is
[tex]\begin{gathered} S_{\infty}=\frac{250}{1-\frac{4}{5}} \\ S_{\infty}=1250 \end{gathered}[/tex]
Therefore the sum is 1250
Hence the it converges
