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Q.

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

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a

1(1−x)2

b

11−x

c

1(1+x)2

d

1(1−x)3

answer is D.

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Detailed Solution

Let S=1+3x+6x2+10x3+…∞xS=x+3x2+6x3+…∞On subtracting,  we getS(1−x)=1+2x+3x2+4x3+…∞x(1−x)S=x+2x2+3x3+…∞Again on subtracting,  we getS[(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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The sum of the series  1+3x+6x2+10x3+…∞ will be