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  • Sum of n terms of the series tan^-1(1/3) +tan^-1(1/7) + tan^-1(1/13) +....... is

Sum of n terms of the series tan^-1(1/3) +tan^-1(1/7) + tan^-1(1/13) +....... is

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Solution:     

               T_r= an^-1(1/1+r(r+1))= an^-1(r+1-r/1+(r+1)r)

         Rightarrow      T_r= an^-1(r+1)- an^-1(r)

    Thus ,      S_n=sum_r=1^nT_r= an^-1(n+1)- an^-11

     Rightarrow     an^-1(n+1-1/1+(n+1)1)= an^-1(n/n+2)

Posted by

Deependra Verma

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