
sum of combinations
Hello ,
I need help to prove that :
(2n)! / (n! * n!) + (2n1)! / ( (n1)! * n! ) + (2n2)! / ( (n2)! * n! ) + ... + n!/( 0! * n!) = (2n+1)! / ( n! * (n+1)! )
or C_{2n}^{n} + C_{2n1}^{n} + ... + C_{n}^{n} =C_{2n+1}^{n+1}
I applied mathematical induction and it didn't work or i did something wrong.
I appreciate your help !

Re: sum of combinations
You need to generalize the statement you are proving. Show $\displaystyle C_m^n+C_{m1}^n+\dots+C_n^n = C_{m+1}^{n+1}$ by induction on m.

Re: sum of combinations
Thank you emakarov , i successfully applied mathematical induction on m .
You really saved me . Thanks.