Proof by Induction - Requires calculus

[mathsgeek]

[SOLVED] Proof by Induction - Requires calculus

I have received a question that i have been trying to do and requires a proof to prove that it is true. The question is here:

http://img401.imageshack.us/my.php?image=23688074ji0.png

I am having some trouble to prove this as at some stage u are required to use differentiation and integration however i do not know homework to accomplish this, could somebody help me get on the right track and start me off for this question as i am having moderate difficulty? thankyou

 

[mathman]

Start with expanding (1+x)ⁿ using the binomial theorem and get
1) (1+x)ⁿ=c₀+c₁x+...c_nxⁿ
Take the first derivative and get
2) n(1+x)^n-1=c₁+...nc_nx^n-1

Finally, let x=1 and add 1 and 2 together to get the desired result.

 

[mathsgeek]

Please delete thread, thankyou