Question

n(n+6n +11 2.3+3.4+4.5+.... to n terms 1 3​

Answer 1

Answer:

The nth term in the given series is (n + 1) (n + 2) Let p(n) be the statement : n(n2 + 6n + 11)/ 3 and let S(n) be the sum on the left hand side. Since S(1) = 2.3 = (1)(1 + 6 + 11)/3 = 6 ∴ The statement is true for n = 1 Assume that the statement p(n) is true for n = k i.e., S(k) = 2.3 + 3.4 +...+ (k + 1) (k + 2) = k(k2 + 6k + 11)/3 We show that the statement is true for n = k + 1 i.e., We show that S(k + 1) = (k + 1) [(k + 1)2 + 6(k + 1) + 11)/3] We observe that S(k + n-n-prove-that-2-3-3-4-4-5-upto-n-terms-n-n-2-6n-11-3