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You are not logged in. #1 20130102 05:06:34
Proofshow would we prove the identity: in algebra? Last edited by cooljackiec (20130102 05:07:38) I see you have graph paper. You must be plotting something #2 20130102 05:40:09
Re: ProofsYou can check that (Expand LHS and show it's equal to RHS.) Hence Adding up … Rearrange, noting that , and you're done. Last edited by scientia (20130102 06:06:36) #3 20130102 06:17:24
Re: ProofsAnother way: We can notice that the number on the RHS is the number of ways to choose r+1 numbers out of the set The sum on the LHS can be interpreted like this: If we know that the greatest number we will choose is r+k (for ), then we can choose the rest of the numbers in ways. If we sum all those values for all different values of k between 1 and nr+1, we will get the total number of ways to choose r+1 numbers from the set mentioned before. But, we also know that that will be the sum on the RHS, so the RHS and the LHS must be equal! Last edited by anonimnystefy (20130102 06:19:47) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20130102 07:09:54
Re: ProofsAlgebraically? I see you have graph paper. You must be plotting something 