Let S_n = _ k=1 ^ 4n (-1)^ k(k+1) 2 k^2. Then S_n can take value(s)

JEE Advanced 2013 Mathematics question

Let . Then can take value(s)

(A)1056Correct
(B)1088
(C)1120
(D)1332Correct

Answer: (A),(D)

Solution

for k = 1, 2, 3, 4 is 1, 3, 6, 10, so the signs follow the pattern −, −, +, + repeating with period 4. Group the terms in fours: 1)^22)^23)^24)^2$ = 2(8m + 4) + 2(8m + 6)

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Question ID VK-026174