As n increases, more and more terms are included, but the terms are smaller and smaller, so the partial sum Sn keeps getting larger, but slows down as it approaches S.

What they're looking for is the first Sn that exceeds 0.95S.

Since Sn=(1-r^n)/(1-r) and S=1/(1-r), you need to have Sn/S=1-r^n=0.95.

- Hollywood