Let
be an increasing function and b ∈ R {\displaystyle {}b\in \mathbb {R} } . Show that the sequence f ( n ) {\displaystyle {}f(n)} , n ∈ N {\displaystyle {}n\in \mathbb {N} } , converges to b {\displaystyle {}b} if and only if
holds, i.e. if the limit of the function for x → + ∞ {\displaystyle {}x\rightarrow +\infty } is b {\displaystyle {}b} .