Binomial ques.. (1 Viewer)

[jsttesting]

Hi,

Can anyone try the following ques and lemme know how it's done...


By giving x appropriate numerical values in the expansion of (1+x)^n, prove that:

n(sigma)k=1 (-2)^k (nCk) = (-1)^n

Thanks.

 

[m_isk]

write out the expansion of (1+x)^n, and then let x=-1. In order to see what you should subsitute, expand out the sigma notation given in the question, and underneath it write out the expansion of the (1+x)^n. By comparison of certain powers of x, or even by simple observation, you will see that substitution x=-1 is the one required.

 

[jsttesting]

Ah ok...lol.....I was wondering how you figure out the substitution, coz I thought there was a method for it.....anwyays....thanks for that..!

 

[m_isk]

y do i sense sarcasm??

 

[jsttesting]

y do i sense sarcasm??

lol....i only meant to say that i was wondering if there was any other method other than plain observation of the two expansions...nothing more...