Question

Solve $2+1+\frac{1}{2}+\frac{1}{4}+.....$

Answer 1

This sequence is an infinite geometric progression with

$r=\frac{1}{2}<1$.

Thus if a is its first term and s its sum, we have

$s=\frac{a}{1-r}=\frac{2}{1-\frac{1}{2}}=4$