To show that $\lim_{n\rightarrow\infty}$ $\frac{n^{2}}{2^{n}} = 0$

Question

We need to show that that $\lim_{n\rightarrow\infty}$ $\frac{n^{2}}{2^{n}} = 0$. This makes sense intuitively since exponentials always rush to infinity faster than do polynomials, but I don't know how to prove it.

Cool thing is, this is actually not from a math class, but from my CS class, where we have to compare runtimes. Regardless, can someone show me how to prove this without using differentiation? Thanks!

score 1 · Accepted Answer · answered Oct 22 '20 at 21:49

1

Hint: Can you show that $0 \le \frac{n^2}{2^n} \le \frac{1}{n}$ for $n \ge 10$?

answered Oct 22 '20 at 21:49

ViktorStein

4,838

@user00000000001899 Try induction or check the great answers on the duplicate question. – ViktorStein Oct 23 '20 at 00:08

To show that $\lim_{n\rightarrow\infty}$ $\frac{n^{2}}{2^{n}} = 0$

1 Answers1