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If sum(r=1)^(n)r(r+1)+sum(r=1)^(n)(r+1)(...

If `sum_(r=1)^(n)r(r+1)+sum_(r=1)^(n)(r+1)(r+2)=(n(an^(2)+bn+c))/(3),(a,b,cinN)` then

A

`a + b + c = 24`

B

`2a + b - c = 0`

C

`a - b + c= 6`

D

`ab + bc + ca = 11`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`overset(n)underset(r=1)sumr(r+1)+overset(n)underset(r=1)sum(r+1)(r+2)`
`=overset(n)underset(r=1)sum2(r+1)^(2)=(n(2n^(2)+9n+13))/(3)`
`rArr (1)/(3)(n+1)(n+2)(n+n+3)`
`rArr (1)/(3)(n+2)(2n+3)(n+1)`
`rArr a_(1) = 1, a_(2) = 2, a_(3) = 3`
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