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  • If ( 4x^2 +1 )^n =sigma ar (1+x^2)^n-r x^2r , then the value of sigma a r is (where lower limit r=0 and upper limit r=n)

If ( 4x^2 +1 )^n =sigma ar (1+x^2)^n-r x^2r , then the value of sigma a r is (where lower limit r=0 and upper limit r=n)

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Solution:  

                (4x^2+1)^n=sum_r=0^na_r(1+x^2)^n-rx^2r

          Dividing  L.H.S  and  R.H.S  by   (1+x^2)

        (1+frac3x^21+x^2)^n=sum_r=0^na_r(fracx^21+x^2)^r

   Rightarrow            a_r=^nc_r3^rRightarrow sum_r=0^na_r=(4)^n

    

                

Posted by

Deependra Verma

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