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  • The coefficient of x^6 in the expansion of (1+x+x^2)^6 is

The coefficient of x^6 in the expansion of (1+x+x^2)^6 is

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Solution:    We have ,   (1+x+x^2)^6

                Rightarrow   [1+x(1+x)]^6=1+^6c_1 x(1+x)+^6c_2x^2(1+x)^2+.....+^6c_6x^6(1+x)^6

                The coefficient of  x^6 is 

               Rightarrow          (^6c_3)(^6c_3)+(^6c_4)(^6c_2)+(^6c_5)(^6c_1)+1

               Rightarrow                   =20+90+30+1=141.

              ecause                    ^nc_r=fracn!(n-r)!r!  

Posted by

Deependra Verma

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