Find upper bound for sequence

Question

$$ Fn = \frac{1}{n+1} +\frac{1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{n+n}$$

I need to show that 1 is an upper bound for this sequence.I tried to use induction but didn't manage to prove it.

Possible duplicate of How do I prove$\frac 34\geq \frac{1}{n+1}+\frac {1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{n+n}$ — Martin R, Feb 03 '19 at 10:43
Also related: https://math.stackexchange.com/q/525749/42969. — Martin R, Feb 03 '19 at 10:44

score 1 · Answer 1 · answered Feb 03 '19 at 10:43

1

Hint: observe that each term in the sum is bounded from above by $\frac{1}{n}$ and there are $n$ terms.

answered Feb 03 '19 at 10:43

Harnak

1 Answers1