Question
If the coefficient of the middle term in the expansion of (1+x)2n+2 is p and the coefficients of middle terms in the expansion of (1+x)2n+1 are q and r, then
Answer: Option C
:
C
Since (n+2)th term is the middle term in the
expansion of (1+x)2n+2, therefore p =2n+2Cn+1.
Since (n+1)th and (n+2)th terms are middle terms in the expansion of (1+x)2n+1,
thereforeq =2n+1Cn and r =2n+1C2n+1.
But ,2n+1Cn +2n+1Cn+1 =2n+2Cn+1
∴ q + r = p
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:
C
Since (n+2)th term is the middle term in the
expansion of (1+x)2n+2, therefore p =2n+2Cn+1.
Since (n+1)th and (n+2)th terms are middle terms in the expansion of (1+x)2n+1,
thereforeq =2n+1Cn and r =2n+1C2n+1.
But ,2n+1Cn +2n+1Cn+1 =2n+2Cn+1
∴ q + r = p
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