The value of $r$ for which $$\binom{20}r\binom{20}0+\binom{20}{r-1}\binom{20}1+\binom{20}{r-2}\binom{20}2+\cdots+\binom{20}0\binom{20}r$$ is maximum is?
I tried to wrap my head around the solution but I don't get it. Could someone help me with it in an easier way? The solution arbitrary begins by considering the expansion of $(1+x)^{20}$ and then multiplying it to itself. A more question-oriented solution would be appreciated. Thanks.
$r$ has to be some sort of plain integer. This whole question isn't about negative or fractional indices.
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