Question

Test for convergence

Answer 1

Since $\frac{1}{2^{n}}$ is a geometric series, for a series like this to converge, its ratio has to be less than 1.

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