Question
1 . The sum of the series 1 + 3x + 6x2 + 10 x3 + ....... ∞ will be
Answer: Option D
:
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)] = 11−x⇒ S =1(1−x)3
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:
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)] = 11−x⇒ S =1(1−x)3
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