finding the value of the sum $\sum _{n=1}^{\infty} \frac{7^{n}}{8^{n}+2^{n}}$ I am concerned with finding the value of the sum $\sum _{n=1}^{\infty}  \frac{7^{n}}{8^{n}+2^{n}}$. There may be some easy way to do this, but I have not found a way to compute this sum, and ones like it. I cannot figure out how to turn it into a single easy-to-calculate exponential, but I am wondering if there is another way. I already know that this sum is convergent, but I want to know exactly how to calculate its value. Any help would be appreciated. 

Hints:
$$\frac{7^n}{8^n+2^n}\le\left(\frac 78\right)^n\;,\;\;\text{and}\;\;\left|\frac 78\right|<1$$
