oh...my questions are challenge enough..wish someone can answer me this binomial theory...i really sucks at this..

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- Sep 17th 2009, 07:35 PMmanusformbinomials...
oh...my questions are challenge enough..wish someone can answer me this binomial theory...i really sucks at this..

Show that,

- Sep 17th 2009, 10:02 PMBingk
Did you copy that correctly?

If it's supposed to be

This was already shown

So,

This gives us - Sep 19th 2009, 04:57 AMOpalg
Sorry to have to say so, but the expression in red makes no sense (nor does the rest of that argument). if k is the summation index, then it cannot also occur as part of one of the limits of summation. The summation index is a variable, and the limits of summation must be constants.

The left side of that identity is the coefficient of in the expression . But that is a geometric series, with sum . To find the coefficient of there, write .

Picking out the coefficient of in , you find that it is

But in the second line of that expression, the sum of all the binomial coefficients is . In the first line, the sum of half of the binomial coefficients (with k going from 0 to n) is . That gives the value for the coefficient of as - Sep 20th 2009, 08:17 PMBingk
Yup, you're absolutely right, I completely missed that :) ... sorry.