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AP EAMCET20228 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual

_ n 1 n [1+ 1 2 + 1 3 + 1 4 + + 1 n ]=

Options

  1. A2
  2. B2
  3. C2 -1
  4. D2 2

Correct answer

B. 2

Step-by-step solution

_ n 1 n [1+ 1 2 + 1 3 + 1 4 + 1 n ] aligned & = _ n 1 n _ r =1 ^ n 1 r = _ n 1 n _ r =1 ^ n 1 ( r n ) n & = _ n ( 1 n ) _ r =1 ^ n 1 r n & = ₀^1 1 x dx ; r n = x & = [ x ^ - 1 2 +1 - 1 2 +1 ]₀^1= [2( x )^ 1 2 ]₀^1=2 aligned

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