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AP EAMCET202018 Sep 2020Morning ShiftMathematicsSequences and SeriesActual

Find ( _ t=1 ³⁹ f(t) ) if (f: R R ) is defined as (f(x+y)=f(x)+f(y), x, y R ) and (f( I )=7 )

Options

  1. A5187
  2. B5460
  3. C5740
  4. D5407

Correct answer

B. 5460

Step-by-step solution

It is given that, (f(x+y)=f(x)+f(y) ) and ( aligned & f(1)=7 & f(x)=7 x aligned ) ( f(x)=7 x ) So, ( aligned _ t=1 ³⁹ f(t) & =7[1+2+3+ +39] & =7 39 40 2 =5460. aligned )

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