After the limit turns to be an equation where \(\displaystyle L=pL\) or another transformation , then :

For p>1 , \(\displaystyle L=\infty\) ; For p<1 \(\displaystyle L=0\)

Example: \(\displaystyle L=\lim_{n\rightarrow \infty} \dfrac{n^2 }{2^n }=\lim_{n\rightarrow \infty} \dfrac{n^2 +2n +1 }{2^{n+1} }=\dfrac{1}{2}L\).

Since \(\displaystyle p=1/2 < 1 \; \Rightarrow L=0\).