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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)` thenA. `a + b + c = 24`B. `2a + b - c = 0`C. `a - b + c= 6`D. `ab + bc + ca = 11` |
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Answer» Correct Answer - 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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