The common ratio of a geometric progression is 0.99. Express the sum of the first 100 terms as a percentage of the sum to infinity, giving your answer correct to 2 significant figures.

Answer 1

sn= a(1-r^n)/(1-r)

s100=a(1-.99^100)/(1-.99)=about a(.634)/.01= 63.4a

sn = a/(1-r) for n=infinity

=a/(1-.99)=a/.01=100a

s100/sn= .634 =about 63%