Home » Past Questions » Mathematics » Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^2, (\frac{9}{10})^3, ...\)...

Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^2, (\frac{9}{10})^3, ...\)...


Question

Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^2, (\frac{9}{10})^3, ...\)

Options

A) \(\frac{1}{10}\)

B) \(\frac{9}{10}\)

C) \(\frac{10}{9}\)

D) \(10\)

The correct answer is D.

Explanation:

Since it's G.P r =T2/a =9/10 /1 =9/10
Sum to infinity is given as
Sum to infinity = a/(1-r)
= 1/(1-9/10)
=1/(1/10)
=1*10/1
=1*10
=10

Explanation provided by Salami Umar


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