Evaluate Part 2

Calculus Level 2

Find a=1(1)a+1(x1)aa\displaystyle \sum_{a=1}^\infty \frac{(-1)^{a+1}(x-1)^a}{a} with interval of convergence (0,2](0,2] and radius of convergence 1.

Note:
1. The link for interval and radius of convergence is here.
2. The log(x)\text{log}(x) in the answer section means log base 10.

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