Maxima of discrete functions involving nPr, nCr, etc?

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SUMMARY

The discussion focuses on proving that the expression 20Cr × 0.1^r × 0.9^(20-r) achieves its maximum value when r equals 2. The user highlights the challenge of differentiating the expression due to the discrete nature of the binomial coefficient nCr. A solution to this problem is referenced from Math Stack Exchange, which provides a method for determining the maximum term in the binomial expansion.

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  • Understanding of binomial coefficients (nCr)
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  • Concept of maximizing functions
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Homework Statement



So I want to prove that the expression 20Cr×0.1r 0.9(20-r) reaches maximum value for r=(0.1)×20=2

Homework Equations

The Attempt at a Solution


I can prove it by trial and error but can't differentiate the expression because nCr isn't continuous.
 
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