Let x n =1 + \frac{1}{2}\: + \frac{1}{3} + \ldots\ldots\ldots..\: + \frac{1}{N}\:\:\:That means, x_{1} = 1,x_{2} = 1 + \frac{1}{2},x_{3} = 1 + \frac{1}{2} + \frac{1}{3} and so on. Then which of the following statements is true?

Correct Answer is : For any integer M, there is an n such that xn ≥ M.

For any integer M, there is an n such that x n ≥ M.

There is an integer m such that x n + 1 < x n for some n ≥ m

For any positive integer m, there is no n such that xn + 1 - x n < 10 -m

MH SET Exam 16 Apr 2017 Paper

Question : 29 of 60

Marks: +1, -0

Let x_n =

1 + \;{1}/{2}\: + \;{1}/{3} + ………..\: + \;{1}/{N}\:\:\:

That means,

x_{1} = 1,x_{2} = 1 + \;{1}/{2},x_{3} = 1 + \;{1}/{2} + \;{1}/{3}

and so on. Then which of the following statements is true?

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