Mathematics

Problem

Let

a

be the first term and

r

the common ratio (

|r|<1

) of a convergent geometric progression. The sum of the first

n

terms is

S_n

and the sum to infinity is

S_{\infty}

. a. (i) Prove that

S_n = \dfrac{a(1-r^{\,n})}{1-r}

.},{