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KVPY2017MathematicsLimits

Let n be the smallest positive integer such that 1+ 1 2 + 1 3 + + 1 n 4 Which one of the following statements is true?

Options

  1. A20 < n 60
  2. B60 < n 80
  3. C80 < n 100
  4. D100 < n 120

Correct answer

A. 20 < n 60

Step-by-step solution

array l 1+x < 1+x+ x² 2 ! + x³ 3 ! + 1+x < e^ x array (1+x) < x x = 1 y (1+ 1 y ) < 1 y (y+1)- y < 1 y put y =1 (2)- (1) < 1 1 put =y=2 3- 2 < 1 2 put =y=3 4- 3 < 1 3 put y=n (n+1)- n < 1 4 (n+1)- (1) < 1+ 1 2 + 1 3 + 1 n (n+1) 4n e⁴-1n 60

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