Question

Test for convergence

Answer 1

Since
`(1)/(2^(n))` is a geometric series, for a series like this to converge, its ratio has to be less than 1.

The ratio is
`|(1)/(2)| < 1`, thus, we can conclude that
`\sum_(n=1)^(\infty) (1)/(2^(n))` will converge (ie has a limiting sum)