Question

tìm giới hanjn

1) lim \(\frac{\left(-1\right)^n}{n-3}\)

2) lim \(\frac{n\left(sin\left(pi.n^2\right)\right)}{n^2+3n-2}\)

Answer 1

1) lim\(\frac{\left(-1\right)^n}{n-3}\)

ta có: \(\left|\frac{\left(-1\right)^n}{n-3}\right|=\frac{1}{n-3}< \frac{1}{n-4}\)

lim \(\frac{1}{n-4}=lim\frac{\frac{1}{n}}{1-\frac{4}{n}}=\frac{lim0}{1}=0\)

2) lim\(\frac{nsin\left(pi.n^2\right)}{n^2+3n-2}\)

ta có : \(\left|\frac{nsin\left(pi.n^2\right)}{n^2+3n-2}\right|\)<=\(\frac{n}{n^2+3n-2}\)

=> lim\(\frac{n}{n^2+3n-2}=0\)

=>lim\(\frac{nsin\left(pi.n^2\right)}{n^2+3n-2}\)=0