Binomial Theorem: 11 Terms Explained

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Discussion Overview

The discussion revolves around the Binomial Theorem, specifically focusing on the expansion and calculation of terms related to the expression involving binomial coefficients and powers. The scope includes mathematical reasoning and exploration of the theorem's application.

Discussion Character

  • Mathematical reasoning, Exploratory

Main Points Raised

  • One participant requests hints for calculating a series involving binomial coefficients and powers of 2.
  • Another participant mentions the need to find the sum of the series.
  • A different participant suggests expanding the expression (1-x)^n, evaluating it at x=2 and n=11, and then taking the integral of the expansion to identify a pattern.
  • A later reply expresses gratitude for the suggestion, indicating engagement with the proposed method.

Areas of Agreement / Disagreement

The discussion does not present a consensus, as participants are exploring different approaches and suggestions without resolving the problem or agreeing on a single method.

Contextual Notes

Participants have not fully detailed their assumptions or the specific steps involved in their reasoning, leaving some mathematical processes and dependencies on definitions unresolved.

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...
 
Expand

(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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