The sum -i-0m 10Ci 20Cm-i is maximum when m is-

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Many-One onto Function

The sum ∑i=...

Question

The sum $\sum_{i = 0}^{m}^{10} C_{i}^{20} C_{m - i}$ is maximum when $m$ is:

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m \sum i = 0 (\frac{10}{i}) (\frac{20}{m - i})

m \sum i = 0 (\begin{matrix} 10 i \end{matrix}) (\begin{matrix} 20 m - i \end{matrix})

m = 15

^{m} C_{r}

r = \frac{m}{2} .

\sum_{i = 0}^{m} (\frac{10}{i}) (\frac{20}{m - i})

(\frac{p}{q}) = 0

The sum $\sum_{i = 0}^{m} (\frac{10}{i}) (\frac{20}{m - i}), w h e r e (\frac{p}{q}) = 0 i f p > q,$ is maximum when m is equal to

m \sum i = 0 (\frac{10}{i}) (\frac{20}{m - i}),

(\frac{p}{q}) = 0

p < q,

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