The sum of the series 1−3x+5x2−7x3+…∞, when |x|<1 is
A
1(1+x)
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B
1(1−x)
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C
1−x(1+x)2
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D
1+x(1−x)2
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Solution
The correct option is C1−x(1+x)2 Let Sn denote the sum of the given infinite series. Now, S∞=1−3x+5x2−7x3+…∞ Here, a=1,r=−x and d=2 ∴S∞=11−(−x)+2(−x)[1−(−x)]2 =11+x−2x(1+x)2 =1−x(1+x)2