Please solve the problem of Binomial theory.
1) Prove that C0+4C1+8C2+12C3+……..+4nCn=1+n2n-1
Since , you only need to prove the following:
Note that:
.... (1)
Differentiate both sides of (1) with respect to x:
.... (2)
(Identity (2) can also be proved using a combinatorial argument)
Now substitute x = 1 into (2). Then multiply both sides by 4 and you get the result.
Is it meant to read
?
This statement is FALSE. Substitute n = 1, for example, to see this.
The correct identity is given (and a solution suggested) in this thread: http://www.mathhelpforum.com/math-he...l-problem.html