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Q.

Sum to n terms of the series 1+(1+2)+(1+2+ 3) +…is

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a

12n(n+1)(n+2)

b

13n(n+1)(n+2)

c

14n(n+1)(2n+1)

d

16n(n+1)(n+2)

answer is D.

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Detailed Solution

tr=1+2+…+r=12r(r+1)=12r2+r∑r=1n tr=1216n(n+1)(2n+1)+12n(n+1)=16n(n+1)(n+2)
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Sum to n terms of the series 1+(1+2)+(1+2+ 3) +…is