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The sum to n terms of the series 12 + 2.22 + 32 + 2.42 + 52 + ........ = n(n + 1)2/2 when n is even. When n is odd, the sum is(a) n2(n + 1)/2(b) n(n2 - 1)/2(c) n(n+1)2 (2n+1)(d) None of these |
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Answer» Correct option (a) n2(n + 1)/2 Explanation: 12 + 2.22 + 32 + 2.42 + 52 + ........ + (2k - 1)2 + 2(2k)2 = 2k(2k + 1)2/2 Let n = 2k + 1 (odd) 12 + 2.22 + 32 + 2.42 + 52 + ........ + (2k - 1)2 + 2(2k)2 + (2k + 1)2 = 2k(2k + 1)2 /2 + (2k + 1)2 = (2k + 1)2 (2k + 2)/2 = n2(n + 1)/2 |
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