how to find sum of the given series

How to find sum of the following series:

$1+\dfrac{1}{3}\dfrac{1}{4}+\dfrac{1}{5}\dfrac{1}{4^2}+...$

The general term is $u_n=\frac{1}{2n+1}\frac{1}{4^n};n\geq 1$

Any help

Answer

HINT:

$$\ln(1+x)=x-\dfrac{x^2}2+\dfrac{x^3}3-\dfrac{x^4}4+\cdots$$

$$\ln(1-x)=-x-\dfrac{x^2}2-\dfrac{x^3}3-\dfrac{x^4}4-\cdots$$

$$\ln(1+x)-\ln(1-x)=?$$

Keep in mind : Taylor series for $\log(1+x)$ and its convergence