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If f: R R satisfies f(x+y)=f(x)+f(y) , for all x, y R and f(1)=7 , then _ r=1 ^n f(r) is

Options

  1. A7 n(n+1) 2
  2. B7 n 2
  3. C7( n +1) 2
  4. D7 n+(n+1)

Correct answer

A. 7 n(n+1) 2

Step-by-step solution

f ( x + y )= f ( x )+ f ( y ) . Let f ( )= m f (1)=7 ; m =7, f ( x )=7 x _ r =1 ^ n f ( r )=7 ₁^ n r = 7 n ( n +1) 2

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