# sum of combinations

• April 19th 2013, 10:49 AM
gambix
sum of combinations
Hello ,
I need help to prove that :
(2n)! / (n! * n!) + (2n-1)! / ( (n-1)! * n! ) + (2n-2)! / ( (n-2)! * n! ) + ... + n!/( 0! * n!) = (2n+1)! / ( n! * (n+1)! )

or C2nn + C2n-1n + ... + Cnn =C2n+1n+1

I applied mathematical induction and it didn't work or i did something wrong.
• April 19th 2013, 12:08 PM
emakarov
Re: sum of combinations
You need to generalize the statement you are proving. Show $C_m^n+C_{m-1}^n+\dots+C_n^n = C_{m+1}^{n+1}$ by induction on m.
• April 19th 2013, 10:33 PM
gambix
Re: sum of combinations
Thank you emakarov , i successfully applied mathematical induction on m .
You really saved me . Thanks.