Show that (nC0 )nC0 -((n+1)C 1) n 1 +((n+2)C2) nC2-..........= (-1)^n

thnks!

Dear Swapnil,

The Binomial Theorem is a quick way (okay, it''s a less slow way) of expanding (or multiplying out) a binomial expression that has been raised to some (generally inconveniently large) power. For instance, the expression (3x – 2)¹⁰ would be very painful to multiply out by hand. Thankfully, somebody figured out a formula for this expansion, and we can plug the binomial 3x – 2 and the power 10 into that formula to get that expanded (multiplied-out) form.

The formal expression of the Binomial Theorem is as follows:

  Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved

Yeah, I know; that formula never helped me much, either. And it doesn''t help that different texts use different notations to mean the same thing. The parenthetical bit above has these equivalents:

Recall that the factorial notation "n!" means " the product of all the whole numbers between 1 and n", so, for instance, 6! = 1×2×3×4×5×6. Then the notation "₁₀C₇" (often pronounced as "ten, choose seven") means:

 



 

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. 

https://www.askiitians.com/packages/packages.aspx


So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert