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  • A function f(x) is given by f(x) = 5^x / 5^x +5 Then the sum of series f(1/20) +f(2/20 ) + ..............+f(39/20) is equal to

A function f(x) is given by f(x) = 5^x / 5^x +5 Then the sum of series f(1/20) +f(2/20 ) + ..............+f(39/20) is equal to

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Solution:   We have ,

                    f(x)=frac5^x5^x+5             .........(1)

    Rightarrow          f(2-x)=frac5^2-x5^2-x+5=frac55^x+5          ........(2)

   From (1)+(2) We get 

   Rightarrow         f(x)+f(2-x)=1

  herefore             f(frac120)+f(frac3920)=1            ecause       frac3920=2-frac120

  Similarly       f(frac220)+f(frac3820)=1

                                 \ .....................\ \ ....................\ \ .....................

   Hence ,          f(frac120)+f(frac220)+..................+f(frac3920)=19+frac12=frac392

                                f(frac2020)=frac12.

   

     

Posted by

Deependra Verma

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