Prove by mathematical induction that $1 + 1/4 +\ldots + 1/4^n \to 4/3$ Please help. I haven't found any text on how to prove by induction this sort of problem: 
$$
 \lim_{n\to +\infty}1 + \frac{1}{4} + \frac{1}{4^2} + \cdots+ \frac{1}{4^n} =  \frac{4}{3}
$$
I can't quite get how one can prove such. I can prove basic divisible "inductions" but not this. Thanks.

After subtracting $1$ this is equivalent to $\frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \cdots = \frac{1}{3}$. Behold:

Image taken from here.
