Question

Is this convergent or divergent and find the sum if possible

Answer 1

SOLUTION

The given series is

$250+200+160+128+\cdots$

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

$r=\frac{4}{5}$

The sum to infinity is:

$S_{\infty}=\frac{a}{1-r}$

Notice that the first term is a=250

Hence the sum to infinity is

$\begin{gathered} S_{\infty}=\frac{250}{1-\frac{4}{5}} \\ S_{\infty}=1250 \end{gathered}$

Therefore the sum is 1250

Hence the it converges