Thread: Another binomial coeffeciant SUMMATION

I believe IMO that summing binomial coefficients is very tricky. there are methods of induction to prove the result, but i think finding a way to come to actual result instead of M.induction is even better.



how to yield this result?? any help would be appreciated. Umm... btw i know the way of induction and yea i have proved it that way, but i want some ways in actually retrieving the result(say if the answer wasn't given).

thank you

I haven't tried it, but the following may work.

Let f(x)=C0x^n - C1x^(n+1) + .... (-1)^n Cnx^2n.

Get a closed form expression for f(x) and then integrate from 0 to 1.

Originally Posted by Heinsbergrelatz

I believe IMO that summing binomial coefficients is very tricky. there are methods of induction to prove the result, but i think finding a way to come to actual result instead of M.induction is even better.



how to yield this result?? any help would be appreciated. Umm... btw i know the way of induction and yea i have proved it that way, but i want some ways in actually retrieving the result(say if the answer wasn't given).

thank you

makes no sense. What is the denominator in each term ?

Originally Posted by DrRocket

Originally Posted by Heinsbergrelatz

I believe IMO that summing binomial coefficients is very tricky. there are methods of induction to prove the result, but i think finding a way to come to actual result instead of M.induction is even better.



how to yield this result?? any help would be appreciated. Umm... btw i know the way of induction and yea i have proved it that way, but i want some ways in actually retrieving the result(say if the answer wasn't given).

thank you

makes no sense. What is the denominator in each term ?

my bad. Let me edit the question

i solved this just last night. okay imo i am weak at dealing with integrals involving combinations, and binomial expansions, so i will pose my working up and if any mistakes are seen please do correct.

okay so from the above question i posed, it leads to this;



then integrate from 1 to 0, like mathman said, then i will get the question i posed. now solving the actual integral is daunting.



bt i realized the main trick behind this whole question was realizing a similar integral and solving it from there.










now bck to the 2nd integral again.