Find the sum of $$ \frac{\text{x}}{\text{x}+1}+\frac{\text{x}^2}{\left( \text{x}+1 \right) \left( \text{x}^2+1 \right)}+\frac{\text{x}^4}{\left( \text{x}+1 \right) \left( \text{x}^2+1 \right) \left( \text{x}^4+1 \right)}+... $$ where $x>1$
This is a question from The Art and Craft of Problem Solving. I tried using partial fraction, but it did not seem plausible for me. Also, I can not spot how to use the condition x>1