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Question

1 . The sum of the series 1 + 3x + 6x2 + 10 x3 + ....... ∞ will be


A

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B

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C

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D

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Solution

The correct option is D


Let S = 1 + 3x + 6x2 + 10 x3 + ....... ∞

⇒ x.S = x + 3x2 + 6x3 + ..........∞

Subtracting S(1-x) = 1 + 2x + 3x2 + 4x3 + ........∞

⇒ x(1 - x)S = x + 2x2 + 3x3 + .........∞

Again subtracting,

⇒ S[(1 - x) - x(1 - x)] = 1 + x + x2 + x3 + ........... ∞

⇒ S[(1 - x)(1 - x)] = 11x ⇒ S = 1(1x)3


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