Correct option: (c) 2
Explanation:
we know [(nCr) / (nCr–1)] = [(n – r + 1) / r]
given: n∑r=1 r ∙ [(nCr) / (nCr–1)]
= n∑r=1 (n – r + 1)
= n∑r=1 (n + 1 – r)
= (n + r – 1) + (n + 1 – 2) (n + 1 – 3) + ------- (n + 1 – n)
= n + (n – 1) + (n – 2) + ----- 1
= sum of terms in A. P.
= (n/2)(1 + n) = (n/2)(n + 1)
∴ k = 2