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AP EAMCET201823 Apr 2018Morning ShiftMathematicsDefinite IntegrationActual

If a and b are positive integers such that b>a , then _ n [ 1 n a + 1 n a+1 + 1 n a+2 + + 1 n b ]=

Options

  1. A( b a )
  2. B( a b )
  3. C(a b)
  4. D(a+b)

Correct answer

A. ( b a )

Step-by-step solution

The given limit aligned & _ x [ 1 n a + 1 n a+1 + 1 n a+2 + + 1 n b ] & = _ x [ 1 n a + 1 n a+1 + 1 n a+2 + + 1 n a+n(b-a) ] & = _ x _ r=0 ^ (b-a) n 1 n a+r = _ x 1 n _ r=0 ^ (b-a) n 1 a+ r n & = ₀^ (b-a) d x a+x & =[ (a+x)]₀^ b-a = (a+b-a)- (a+0) & = b- a= b a aligned

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