Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^{2}, (\frac{9}{10})^{3}\)
A
\(\frac{1}{10}\)
B
\(\frac{9}{10}\)
C
\(\frac{10}{9}\)
D
10
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(S_{\infty} = \frac{a}{1 - r}\) (Sum to infinity of a G.P)
\(a = 1; r = \frac{9}{10}\)
\(S_{\infty} = \frac{1}{1 - \frac{9}{10}}\)
= \(\frac{1}{\frac{1}{10}} = 10\)
Source: Myschool Past Questions Archive (Record #30919)