The question is asking about the set $A$ of values of $x$ for which the following series converges pointwise:
$$\sum_{n = 1}^{\infty} \frac{1}{(x + n)(x+n-1)} $$
A part of the answer is given below:
But I do not know why he defined the set A to be like this, could anyone explain this for me please?
Also I can see that the answer is dealing with the following series instead:
$$\sum_{n = 1}^{\infty} \frac{1}{(x + n)(x+ n + 1)} $$
Will this affect the value of $x$ and is this value of $x$ applicable for the first series I mentioned above?
EDIT:
I think there is a typo and the set A should not contain $\pi$ ....... am I correct?