A) \[n+3\]
B) \[n+1\]
C) \[n+2\]
D) \[n\]
Correct Answer: B
Solution :
pth term \[={{T}_{p}}={}^{n}{{C}_{p-1}}{{(x)}^{n-p+1}}{{(1)}^{p-1}}=p\] (p + 1)th term \[={{T}_{p+1}}={}^{n}{{C}_{p}}{{(x)}^{n-p}}{{(1)}^{p}}=q\] Then, coefficient of \[\frac{p}{q}=\frac{{}^{n}{{C}_{p-1}}}{{}^{n}{{C}_{p}}}\] Þ \[\frac{p}{q}=\frac{n!}{\left( p-1 \right)\,!\,\left( n-p+1 \right)\,\,!}\,.\,\frac{p\,!\,\,\,\left( n-p \right)\,\,!}{n\,!}\] Þ \[\frac{p}{q}=\frac{p}{n-p+1}\] Þ \[p+q=n+1\].You need to login to perform this action.
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