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AP EAMCET2008MathematicsSequences and Series

For any integer n 1 , the sum _ k=1 ^n k(k+2) is equal to

Options

  1. An(n+1)(n+2) 6
  2. Bn(n+1)(2n+1) 6
  3. Cn(n+1)(2n+7) 6
  4. Dn(n+1)(2n+9) 6

Correct answer

C. n(n+1)(2n+7) 6

Step-by-step solution

Now, aligned & _ k=1 ^n k(k+2) & = _ k=1 ^n (k^2+2 k )= _ k=1 ^n k^2+2 _ k=1 ^n k & = n(n+1)(2 n+1) 6 + 2 n(n+1) 2 & =n(n+1) ( 2 n+1 6 +1 ) & = n(n+1)(2 n+7) 6 aligned

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