Definite integral/From 1 over n+1 to 1 over n/Exercise

Let ${}f\colon [0,1]\rightarrow \mathbb {R}$ be a continuous function. Consider the following sequence

${}a_{n}:=\int _{\frac {1}{n+1}}^{\frac {1}{n}}f(t)dt\,.$

Determine whether this sequence converges and, in case, determine its limit.

Create a solution