Question

# In the expansion of $$(1+x)^n$$ the coefficients of $$p^{th}$$ and $$(p+1)^{th}$$ terms are respectively $$p$$ and $$q$$ then $$p+q =$$

A
n
B
n+1
C
n+2
D
n+3

Solution

## The correct option is B $$n+1$$Binomial Coefficient of $$p^{th}$$ term $$\:^nC_{p-1}=p$$Binomial Coefficient of $$(p+1)^{th}$$ term $$\:^nC_{p}=q$$Therefore, with respect to the above question.$$\dfrac{\:^nC_{p-1}}{\:^nC_{p}}=\dfrac{p}{q}$$$$\dfrac{n!(n-p)!p!}{n!(n-p+1)!(p-1)!}=\dfrac{p}{q}$$$$\dfrac{p}{n-p+1}=\dfrac{p}{q}$$$$n-p+1=q$$$$n=p+q-1$$$$n+1=p+q$$Hence answer is $$n+1$$Mathematics

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