The series of $\sum\limits_{j=0}^{\infty} (\frac{1}{2})^{2j}$

Question

The series converge:

$$\sum_{j=0}^{\infty} \left( \frac{1}{2} \right)^{2j}$$

I try to put it in geometric series but I am stuck some help please.

Answer 1

$$\sum_{j=0}^{\infty} (\frac{1}{2})^{2j}=\sum_{j=0}^{\infty} (\frac{1}{4})^{j}$$ which is a geometric series and converges because $\frac{1}{4} <1$.

Answer 2

$(1/2)^{2j}=[(1/2)^2]^j$ should get you there...

Answer 3

Hint: $(\frac12)^{2j}=(\frac14)^j$