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7.Binomial Theorem
medium
$\left( {\begin{array}{*{20}{c}}n\\0\end{array}} \right) + 2\,\left( {\begin{array}{*{20}{c}}n\\1\end{array}} \right) + {2^2}\left( {\begin{array}{*{20}{c}}n\\2\end{array}} \right) + ..... + {2^n}\left( {\begin{array}{*{20}{c}}n\\n\end{array}} \right)$ का मान होगा
A
${2^n}$
B
$0$
C
${3^n}$
D
इनमें से कोई नहीं
Solution
${(1 + x)^n} = {}^n{C_0} + x.{}^n{C_1} + {x^2}.{}^n{C_2} + …. + {x^n}.{}^n{C_n}$
$x = 2$ रखने पर,
${3^n} = {}^n{C_0} + 2.{}^n{C_1} + {2^2}.{}^n{C_2} + {2^3}.{}^n{C_3} + …. + {2^n}{.^n}{C_n}$.
Standard 11
Mathematics
