Let the n t h term of a series be given by t n = n 2 - n - 2 n 2 + 3 n , n ≥ 3 . The product t 3 t 4 t 5 . . . . . t 50 is equal to

Question

Let the n t h term of a series be given by t n = n 2 - n - 2 n 2 + 3 n , n ≥ 3 . The product t 3 t 4 t 5 . . . . . t 50 is equal to, 1 5 2 ⋅ 7 ⋅ 13 ⋅ 53, 1 5 ⋅ 7 2 ⋅ 12 ⋅ 53, 1 5 2 ⋅ 7 ⋅ 12 ⋅ 51, 1 5 ⋅ 7 2 ⋅ 13 ⋅ 53

MARKS App · Accepted Answer

t n = n - 2 n + 1 n n + 3 t 3 t 4 t 5 . . . t n = 1 ⋅ 4 3 ⋅ 6 2 ⋅ 5 4 ⋅ 7 3 ⋅ 6 5 ⋅ 8 . . . n - 3 n n - 1 n + 2 n - 2 n + 1 n n + 3 = 1 ⋅ 4 ⋅ 2 ⋅ 5 n - 1 n + 2 n n + 3 Put n = 50 we get, 1 ⋅ 4 ⋅ 2 ⋅ 5 49 ⋅ 52 ⋅ 50 ⋅ 53 = 1 7 2 ⋅ 5 ⋅ 13 ⋅ 53

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