a)Find a formula for
$$\frac 1 2 + \frac 1 4 + \frac 1 8 + \cdots + \frac1{2^n}$$
by examining the values of this expression for small values of $n$.
b) Prove the formula you conjectured in part a.
If you can help me with part a, I would really appreciate it. I know how to prove it. I just can't find a formula to the first question.
Thanks.
HINT:
$$\begin{align*} \frac12&=\frac12=1-\frac12\\ \frac12+\frac14&=\frac34=1-\frac14\\ \frac12+\frac14+\frac18&=\frac78=1-\frac18 \end{align*}$$