If \[{{(1+x)}^{15}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+......+{{C}_{15}}{{x}^{15}},\] then \[{{C}_{2}}+2{{C}_{3}}+3{{C}_{4}}+....+14{{C}_{15}}=\] [IIT 1966]

If \[{{(1+x)}^{15}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+......+{

1.	If \[{{(1+x)}^{15}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+......+{{C}_{15}}{{x}^{15}},\] then \[{{C}_{2}}+2{{C}_{3}}+3{{C}_{4}}+....+14{{C}_{15}}=\] [IIT 1966]
A.	\[{{14.2}^{14}}\]
B.	\[{{13.2}^{14}}+1\]
C.	\[{{13.2}^{14}}-1\]
D.	None of these
Answer» C. \[{{13.2}^{14}}-1\]

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If \[{{(1+x)}^{15}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+......+{{C}_{15}}{{x}^{15}},\] then \[{{C}_{2}}+2{{C}_{3}}+3{{C}_{4}}+....+14{{C}_{15}}=\] [IIT 1966]

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