Answer to Question #311005 in Real Analysis for Dhruv rawat

Question

Every montonically increasing sequence are convergent. True or false with full explanation

Answer 1

For a sequence to converge, it has to be monotonic and bounded.

Let us consider the sequence below

$U_{n}=n+1$

We know that $(U_{n})$ is monotonically increasing, but $(U_{n})$ has no upper bound. Thus, $(U_{n})$ does not converge.

Hence, $(U_{n})$ is not convergent