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Question

The sum of the series 13x+5x27x3+, when |x|<1 is

A
1(1+x)
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B
1(1x)
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C
1x(1+x)2
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D
1+x(1x)2
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Solution

The correct option is C 1x(1+x)2
Let Sn denote the sum of the given infinite series. Now,
S=13x+5x27x3+
Here, a=1, r=x and d=2
S=11(x)+2(x)[1(x)]2
=11+x2x(1+x)2
=1x(1+x)2

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