∑r=0mn+rcr is equal to | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

∑r=0mn+rcr is equal to

A

(A) n + m + 1Cn + 1

B

(B) n + m + 2Cn

C

(C) n + m + 3Cn - 1

D

(D) None of these

Answer

(A) n + m + 1Cn + 1

Explanation

Solution

Explanation:
∑r=0mn+rC=πC0+n+1C1+n+2C2+n+3C3+……+n+mCm=n+3C2+n+3C3+……+n+mCm=n+mCm−1+n+mCm=n+m+1Cm=n+m+1Cn+1