What is the sum of the series nCr . 2r?

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Discussion Overview

The discussion centers around the sum of the series involving binomial coefficients, specifically the expression Σ nCr · 2r, where r ranges from 0 to n. The participants explore the mathematical formulation and potential simplifications of this series.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks for the sum of the series Σ nCr · 2r.
  • Another participant provides a hint suggesting a reformulation of the series using the identity Σ nCr · 2r = Σ nCr · 2r · 1n-r.
  • Subsequent posts express gratitude for the hint and information shared.

Areas of Agreement / Disagreement

The discussion does not present any explicit agreement or disagreement on the sum of the series, as the focus is primarily on the initial question and a hint provided.

Contextual Notes

The discussion lacks detailed exploration of the mathematical steps involved in deriving the sum, and the implications of the hint are not fully elaborated upon.

cgchayan
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what will be the sum of this series?
[tex]\Sigma[/tex] nCr . 2r
where r = 0 to n
 
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Hint:
[tex] \sum_{r=0}^n _nC_r \cdot 2^r = \sum_{r=0}^n _nC_r \cdot 2^r \cdot 1^{n-r}[/tex]
 
thanx
 
thanks for sharing information...
 

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