Answer
(b) is not the same as (a) and (c)
Work Step by Step
a) \begin{equation}\sum_{k=2}^{4}\frac{(-1)^{k-1}}{k-1}=\frac{(-1)^{2-1}}{2-1}+\frac{(-1)^{3-1}}{3-1}+\frac{(-1)^{4-1}}{4-1}=\frac{(-1)^{1}}{1}+\frac{(-1)^{2}}{2}+\frac{(-1)^{3}}{3}=-1+\frac{1}{2}-\frac{1}{3}\end{equation}
b) \begin{equation}\sum_{k=0}^{2}\frac{(-1)^{k}}{k+1}=\frac{(-1)^{0}}{0+1}+\frac{(-1)^{1}}{1+1}+\frac{(-1)^{2}}{2+1}=1-\frac{1}{2}+\frac{1}{3}\end{equation}
c) \begin{equation}\sum_{k=-1}^{1}\frac{(-1)^{k}}{k+2}=\frac{(-1)^{-1}}{-1+2}+\frac{(-1)^{0}}{0+2}+\frac{(-1)^{1}}{1+2}=-1+\frac{1}{2}-\frac{1}{3}\end{equation}
(b) is not equivalent to the other two.