Calculate the limit of $(3^n-2^n)^{1/n}$

Asked Nov 21 '19 at 20:10

Active Nov 21 '19 at 21:28

Viewed 50 times

How can I calculate this?

$$\lim_{x\to \infty}\sqrt[n] {3^n-2^n} $$ I calculated the answer with Matlab and i know that it is 3 and thought that it has to be solved with Sandwich rule. I found an upper limit (3), but I haven't been able to find a sequence, which limit is 3, but it is smaller than the given sequence;

edited Nov 21 '19 at 21:28

QC_QAOA

11,796

asked Nov 21 '19 at 20:10

csillagu

1

HINT: This is simply $$3 \cdot \sqrt[n]{1-\left( \frac{2}{3}\right)^n}$$ – Crostul Nov 21 '19 at 20:13

Calculate the limit of $(3^n-2^n)^{1/n}$

0 Answers0