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If the coefficient of the middle term in the expansion of (1+x)^{2 n+2} is p and the coefficients of middle terms in the expansion of (1+x)^{2 n+1}  are q and r, then
 

Option: 1

p+q=r


Option: 2

p+r=q


Option: 3

p=q+r


Option: 4

p+q+r=0


Answers (1)

best_answer

Since (n+2)^{\text {th }} term is the middle term in the expansion of (1+x)^{2 n+2},  therefore p={ }^{2 n+2} C_{n+1}. Since (n+1)^{\text {th }} and (n+2)^{\text {th }} terms are middle terms in the expansion of (1+x)^{2 n+1}, therefore q={ }^{2 n+1} C_n and r={ }^{2 n+1} C_{n+1} 

But { }^{2 n+1} C_n+{ }^{2 n+1} C_{n+1}={ }^{2 n+2} C_{n+1}

\therefore q+r=p

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vinayak

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