Number of greatest binomial coefficients in the expansion of $(1 + x)^{2 n}$ and $(1 + x)^{2 n + 1}$ are p and q respectively (where n is a positive integer). Find the value of p+2q

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Solution

Middle term has the greatest binomial coefficient in any binomial expansion. When the power is even (in the case of $(1 + x)^{2 n})$ , there will be only one middle term
$\Rightarrow$ Only one term with greatest binomial coefficient.
$\Rightarrow$ p=1
When the power is odd (in the case of $(1 + x)^{2 n})$ , there will be two middle terms terms (or two terms with greatest binomial coefficient)
$\Rightarrow$ q=2
$\Rightarrow$ p+2q=1+4=5

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Number of greatest binomial coefficients in the expansion of (1+x)2n and (1+x)2n+1 are p and q respectively (where n is a positive integer). Find the value of p+2q ___

Number of greatest binomial coefficients in the expansion of $(1 + x)^{2 n}$ and $(1 + x)^{2 n + 1}$ are p and q respectively (where n is a positive integer). Find the value of p+2q

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