If ∑ n = 1 5 1 n n + 1 n + 2 n + 3 = k 3 , then k is equal to:

Question

If ∑ n = 1 5 1 n n + 1 n + 2 n + 3 = k 3 , then k is equal to:, 55 336, 17 105, 19 112, 1 6

MARKS App · Accepted Answer

T n = 1 3 n + 3 - n n ( n + 1 ) ( n + 2 ) ( n + 3 ) = 1 3 1 n ( n + 1 ) ( n + 2 ) - 1 n + 1 n + 2 n + 3 ∑ n = 1 5 T n = 1 3 1 1 · 2 · 3 - 1 2 · 3 · 4 + 1 2 · 3 · 4 - 1 3 · 4 · 5 … + 1 5 · 6 · 7 - 1 6 · 7 · 8 = 1 3 1 6 - 1 6 · 56 = 1 3 56 - 1 336 = 55 3 336 = k 3 ⇒ k = 55 336

Search any question & find its solution

Looking for more such questions to practice?