Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\)
A
10
B
9
C
10/9
D
9/10
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
a = 1, r =\(\frac{9}{10}\)
S\(_n\) = \(\frac{a}{1 - r}\)
S\(_n\) = \(\frac{1}{1-\frac{9}{10}}\)
= 1\(\div \frac{1}{10}\)
=1\(\times \frac{10}{1}\) = 10
Source: Myschool Past Questions Archive (Record #9321)