If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+{{C}_{n}}{{x}^{n}}\], then \[\frac{{{C}_{1}}}{{{C}_{0}}}+\frac{2{{C}_{2}}}{{{C}_{1}}}+\frac{3{{C}_{3}}}{{{C}_{2}}}+....+\frac{n{{C}_{n}}}{{{C}_{n-1}}}=\] [BIT Ranchi 1986; RPET 1996, 97]

If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+

1.	If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+{{C}_{n}}{{x}^{n}}\], then \[\frac{{{C}_{1}}}{{{C}_{0}}}+\frac{2{{C}_{2}}}{{{C}_{1}}}+\frac{3{{C}_{3}}}{{{C}_{2}}}+....+\frac{n{{C}_{n}}}{{{C}_{n-1}}}=\] [BIT Ranchi 1986; RPET 1996, 97]
A.	\[\frac{n(n-1)}{2}\]
B.	\[\frac{n(n+2)}{2}\]
C.	\[\frac{n(n+1)}{2}\]
D.	\[\frac{(n-1)(n-2)}{2}\]
Answer» D. \[\frac{(n-1)(n-2)}{2}\]

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If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+..........+{{C}_{n}}{{x}^{n}}\], then \[\frac{{{C}_{1}}}{{{C}_{0}}}+\frac{2{{C}_{2}}}{{{C}_{1}}}+\frac{3{{C}_{3}}}{{{C}_{2}}}+....+\frac{n{{C}_{n}}}{{{C}_{n-1}}}=\] [BIT Ranchi 1986; RPET 1996, 97]

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