calculus - Prove the series $sum_{n=1}^{infty} a_n$ converges iff $sum_{n=100}^{infty} a_n$ converges

I just had this problem on a final and I was confused about proving the reverse direction. For example, what if $a_n = \frac{1}{(n-1)^2}$?

Then $\sum_{n=100}^{\infty} a_n$ would converge, but the first term in $\sum_{n=1}^{\infty} a_n$ would be undefined.

I think I'm missing something. Any help would be appreciated.