Left( {begin{array}{*{20}{c}}n0end{array}} right) + 2,left( {begin{array}{*{20}{c}}n1end{array}} rig

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7.Binomial Theorem

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$\left( {\begin{array}{{20}{c}}n\\0\end{array}} \right) + 2\,\left( {\begin{array}{{20}{c}}n\\1\end{array}} \right) + {2^2}\left( {\begin{array}{{20}{c}}n\\2\end{array}} \right) + ..... + {2^n}\left( {\begin{array}{{20}{c}}n\\n\end{array}} \right)$ 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

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