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Ex 9.4, 1 - Find sum of series 1 x 2 + 2 x 3 + 3 x 4 - Finding sum from nth number

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.4, 1 Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + … Step 1: Find nth term (an) Here, an = n ( n + 1) = n2 + n Step 2: Finding sum of n terms = (n(n+1)(2n+1))/6 + (n(n+1))/2 = (n(n+1))/2 (((2n+1))/3 " + 1" ) = (n(n+1))/2 ((2n + 1 +3)/3) = (n(n+1))/2 ((2n + 4)/3) = n(n+1)/(2 × 3) [2(n + 2)] = (2n(n + 1)(n + 2))/6 Thus, the required sum is (2n(n + 1)(n + 2))/6

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