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# 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)
$$10$$

### 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

## Discussion (2)

• The answer is D. a/1-r. 1/0.1=10

• 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