Find the taylor series centered at 0 for x 1 - x2 using

Question

1. Find the Taylor series centered at 0 for 1/ (1 - x).

2. Find the Taylor series centered at 0 for x / (1 - x)² using the derivative of the series from (1). Find its radius and interval of convergence.

3. Use your answer to part (2) to calculate the exact value of (1/2) + (2/4) + (3/8) + (4/16) + ···.