If the sum 3 1 2 + 5 1 2 + 2 2 + 7 1 2 + 2 2 + 3 2 + ..... + up to 20 terms is equal to k 2 1 , then k is equal to

Question

If the sum 3 1 2 + 5 1 2 + 2 2 + 7 1 2 + 2 2 + 3 2 + ..... + up to 20 terms is equal to k 2 1 , then k is equal to, 240, 120, 60, 180

MARKS App · Accepted Answer

S 20 = 3 1 2 + 5 1 2 + 2 2 + 7 1 2 + 2 2 + 3 2 + .... + up to 20 terms = Σ r = 1 20 2r + 1 1 2 + 2 2 + 3 2 + .... r 2 = Σ r = 1 20 2r + 1 r 6 r + 1 2r + 1 = 6 Σ r = 1 20 1 r r + 1 = 6 Σ r = 1 20 1 r - 1 r + 1 = 6 1 1 - 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + .... + 1 20 - 1 21 = 6 1 - 1 21 = 6 × 20 21 = 1 20 21 = k 21 k = 120

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