If f(x)=5×5+5x, then the value of f120+f220+…+f3920 is

If f(x)=5x5+5x, then the value of f120+f220++f3920 is

  1. A

    20

  2. B

    292

  3. C

    192

  4. D

    392

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    Solution:

    We have,

    f(x)=5x5+5xf(2x)=52x5+52x=255x+1+52=55x+5

     f(x)+f(2x)=1 for all x

    Now,

    f120+f220+..f3820+f3920=f120+f3920+f220+f3820++f1920+f2120+f2020=1×19+f(1)=19+55+5=392

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