Question

The first term if geometric series is $100$ and the third term is $1$. find the sum of infinity of each of the possible series?

Answer 1

Let the common ratio be $r$.
Given: $100r^2=1$
$⟹r=\pm \frac{1}{10}$
Formula for sum of infinite GP: $\frac{a}{1-r}$ when $|r|<1$
Therefore, the possible sums are:
$\frac{100}{1-1/10}$, $\frac{100}{1+1/10}$
$=\frac{100}{9/10}$, $\frac{100}{11/10}$
$=\frac{1000}{9},\frac{1000}{11}$