If 1+ displaystyle∑ r =1 n n + r C r = 25 C 13, n ∈ N, then the value of n equals

Question

If 1+ displaystyle∑ r =1 n n + r C r = 25 C 13, n ∈ N, then the value of n equals (A) 10 (B) 11 (C) 12 (D) 13

Tardigrade Admin · Accepted Answer

1+ n+1 C1+ n+2 C2+ ldots . .+ n+n Cn= 25 C13 ⇒ 1+2 n Cn= 25 C13 ⇒ n=12

Q. If $1 + r = 1 \sum n^{n + r} C_{r} =^{25} C_{13}, n \in N$ , then the value of $n$ equals