# Induction proof concerning a sum of binomial coefficients: $\sum_{j=m}^n\binom{j}{m}=\binom{n+1}{m+1}$ [duplicate]

I'm looking for a proof of this identity but where j=m not j=0

http://www.proofwiki.org/wiki/Sum_of_Binomial_Coefficients_over_Upper_Index

$$\sum_{j=m}^n\binom{j}{m}=\binom{n+1}{m+1}$$

## marked as duplicate by user147263, Davide Giraudo, Najib Idrissi, Aaron Maroja, Jack D'AurizioApr 8 '15 at 15:56

• To clarify what you mean: you want a proof of $$\sum_{j=m}^n\binom{j}{m}=\binom{n+1}{m+1}$$ correct? – Zev Chonoles Oct 22 '11 at 15:02
• (-1) ${}{}{}{}{}{}$ – The Chaz 2.0 Dec 21 '11 at 16:14

It seems to me that you are looking for the proof of the identity: $$\sum_{j=m}^n\binom{j}{m}=\binom{n+1}{m+1}$$
Hint: what is $\binom{2}{4}$? what is $\binom{n-1}{n}?$