How should I solve this limits of a series which goes to infinity

Question

How can I determinate

$$\lim_{n\to \infty}{\frac{\sum_{i=1}^n\sinh\big(\frac{i}{n}\big)}{\sum_{i=1}^n\cosh\big(\frac{i}{n}\big)}}$$

I can't solve how should I solve this? Thank you.

Answer 1

Hint: Multiply numerator and denominator by $\frac1n$ and you'll recognize two Riemann sums.