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  • The value of 2 (nC1) + 2^3 ( nC3) +2^5 (nC5)+............ is

The value of 2 (nC1) + 2^3 ( nC3) +2^5 (nC5)+............ is

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Solution:   We have  ,  

                   frac12[(1+x)^n-(1-x)^n]=C_1x+C_3x^3+C_5x^5+.........

                  Putting  x=2 on both side , we get the desired result.

             Rightarrow        2 imes C_1+2^3 imes C_3+2^5 imes C_5+.......=frac3^n-(-1)^n2.

Posted by

Deependra Verma

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