1.1: Finite and infinite sums of a geometric series

4PM1/1/June/2022 — Question 4 · 7 marks

The common ratio of a geometric series G\displaystyle G is positive.
The sum of the first 4 terms of G\displaystyle G is 80\displaystyle 80.
The sum to infinity of G\displaystyle G is 81\displaystyle 81.
Show that the sum of the first 7 terms of G\displaystyle G differs from the sum to infinity of G\displaystyle G by
127.\frac{1}{27}.
(7)