Binomial Theorem: 11 Terms Explained

AI Thread Summary
The discussion focuses on applying the Binomial Theorem to find the sum of a series involving binomial coefficients and powers of 2, specifically up to 12 terms. Participants suggest expanding (1-x)^n for n=11 and substituting x=2 to analyze the resulting series. The conversation emphasizes recognizing patterns in the expansion and integrating it to derive further insights. The approach encourages exploring mathematical relationships within the binomial expansion. Ultimately, the exchange aims to clarify the process of summing the series using the Binomial Theorem.
Ananya0107
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Any hints for this
: 1- (11C1/2.3 ).2^2 + (11C2/3.4 ). 2^3 ...so on up to 12 terms .
 
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We have to find the sum...
 
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(1-x)^n and consider this expansion when x=2 and n=11. Now take the integral of the expansion, do you see a pattern emerging? Can you take it from there?
 
Yes, thanks
 

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