Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This question already has an answer here:

I am asked to prove this given $1 \le m \le n - 1$ (homework question):

$$\frac{n!}{(m-1)!(n-m+1)!} + \frac{n!}{m!(n-m)!} = \frac{(n+1)!}{m!(n+1-m)!}$$

Which proof technique should I use to solve this? I tried induction but couldn't seem to get anywhere with it. Maybe I am just bad with factorial, should I use induction?

share|cite|improve this question

marked as duplicate by sandwich, Daniel W. Farlow, Servaes, Michael Medvinsky, Najib Idrissi Dec 6 '15 at 12:16

This question was marked as an exact duplicate of an existing question.

    
    
Multiply top and bottom of first guy by $m$, of second guy by $n-m+1$. Add. – André Nicolas Nov 7 '11 at 17:57
up vote 0 down vote accepted

$$\frac{n!\cdot m}{m(m-1)!(n+1-m)!}+\frac{n!\cdot (n+1-m)}{m!(n+1-m)!}=\frac{m \cdot n!+(n+1)n!-m\cdot n!}{m!(n+1-m)!}=$$

$$=\frac{(n+1)!}{m!(n+1-m)!}$$

share|cite|improve this answer
    
Leave something to the imagination; it is homework :-) – robjohn Nov 7 '11 at 18:40

Not the answer you're looking for? Browse other questions tagged or ask your own question.