Question

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

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

Solution

## The correct option is D $$n+1$$Given, $$p^{th}$$ and $$(p+1)^{th}$$ terms are $$p$$ and $$q$$$${ n }_{ { c }_{ p }-1 }=p,{ n }_{ { c }_{ p } }=q\quad$$$$\Rightarrow \cfrac { q }{ p } =\cfrac { { n }_{ { c }_{ p } } }{ { n }_{ { c }_{ p }-1 } } =\cfrac { n-p+1 }{ p }$$$$\Rightarrow p+q=n+1$$Mathematics

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