Answer the following questions related to the sum of a geometric progression (GP):
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Answer the following questions related to the sum of a geometric progression (GP):
(i) State the standard formula for the sum of the first n terms of a GP whose common ratio is not 1.
(ii) Give a clear reason why this formula is not directly applicable when the common ratio equals 1.
(iii) For a GP whose first term is 8 and common ratio is 1, write its first five terms and obtain an expression for the sum of its first n terms.
(iv) Compare your result from part (iii) with the expression stated in part (i) when r→1. What do you observe?