Find the Taylor series expansion for the function f(x)=(x−1)ln(x)f(x) = (x-1) \ln(x)f(x)=(x−1)ln(x) centered at a=1a = 1a=1.
∑n=2∞(−1)n(x−1)nn−1\sum_{n=2}^{\infty} \frac{(-1)^n (x-1)^n}{n-1}∑n=2∞n−1(−1)n(x−1)n
∑n=1∞(−1)n−1(x−1)n+1n+1\sum_{n=1}^{\infty} \frac{(-1)^{n-1} (x-1)^{n+1}}{n+1}∑n=1∞n+1(−1)n−1(x−1)n+1
∑n=2∞(−1)n−1(x−1)nn\sum_{n=2}^{\infty} \frac{(-1)^{n-1} (x-1)^n}{n}∑n=2∞n(−1)n−1(x−1)n
∑n=1∞(−1)n−1(x−1)nn\sum_{n=1}^{\infty} \frac{(-1)^{n-1} (x-1)^n}{n}∑n=1∞n(−1)n−1(x−1)n