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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