Soit \(\displaystyle\left( a_n\right) _{n\geqslant 1}\) la suite définie par
\[
a_n=(-1)^{n+1}+\left(-\dfrac{1}{2}\right)^{n}+\dfrac{3}{n}\,.
\]
Alors:
\(\displaystyle\liminf_{n\rightarrow \infty }a_n=-\tfrac{1}{4}\ \) et \(\displaystyle\limsup_{n\rightarrow \infty }a_n=\tfrac{3}{2}\)
\(\displaystyle\liminf_{n\rightarrow \infty }a_n=-1\ \) et \(\displaystyle\limsup_{n\rightarrow \infty }a_n=1\)
\(\displaystyle\liminf_{n\rightarrow \infty }a_n=-1\ \) et \(\displaystyle\limsup_{n\rightarrow \infty }a_n=\tfrac{3}{2}\)
\(\displaystyle\liminf_{n\rightarrow \infty }a_n=\tfrac{3}{4}\ \) et \(\displaystyle\limsup_{n\rightarrow \infty }a_n=\tfrac{7}{2}\)