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KCET2011MathematicsSequences and Series

The sum of the first n terms of 1² 1 + 1²+2² 1+2 + 1²+2²+3² 1+2+3 + is

Options

  1. An²-2 n 3
  2. B2 n²+n 3
  3. Cn(n+2) 3
  4. D2 n²-n 3

Correct answer

C. n(n+2) 3

Step-by-step solution

Given series, 1² 1 + 1²+2² 1+2 + 1²+2²+3² 1+2+3 + The n th terms of the series is T_ n = n² n = n(n+1)(2 n+1) 6 n(n+1) 2 = (2 n+1) 3 Now, S_ n = 1 3 ( n+ 1) aligned &= 1 3 2 n(n+1) 2 +n = n 3 (n+1+1) &= n(n+2) 3 aligned

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