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Question

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


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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)2n), there will be only one middle term
Only one term with greatest binomial coefficient.
p=1
When the power is odd (in the case of (1+x)2n), there will be two middle terms terms (or two terms with greatest binomial coefficient)
q=2
p+2q=1+4=5


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