Answer
See below.
Work Step by Step
See text: last paragraph of section 2, with subheading "Reindexing".
Reindexing a series does not alter its convergence, as long as we preserve the order of its terms.
An example is reindexing a geometric sequence converting from
$\displaystyle \sum_{n=1}^{\infty}r^{n-1}$ to $\displaystyle \sum_{n=0}^{\infty}r^{n}$.
Both expressions represent the same sum of terms,
$1+r+r^{2}+r^{3}+...$
but the starting index $n=0$ has a simpler term under the summation.
We could have written this as
$\displaystyle \sum_{n=7}^{\infty}r^{n-7},\ \displaystyle \sum_{n=-2}^{\infty}r^{n+2}$
We select indices so that the general term in the summation expression is as simple as possible.
