T4
Pro následující posloupnosti najděte inf{an }∞ n=1 , sup{an }n=1 a vypočítejte \( \lim_{n \to \infty} \inf a_n \) , \( \lim_{n \to \infty} \sup a_n \) :
38.
\(a_n = \frac{1}{n} \) lim 1/n as n->infinity series 1/n
39.
\(a_n = 1 − \frac{1}{n} \) lim 1 - 1/n as n->infinity
40.
\(a_n = \frac{(-1)^n}{n} \) lim (-1)^n / n as n->infinity
41.
\(a_n = −n \) lim -n as n->infinity
42.
\(a_n = (−1)^{n−1} (2 + \frac{3}{n}) \)
43.
\(a_n = (−1)^n n \)
lim -1^n n as n->infinity
44.
\(a_n = n^{(−1)^n} \)
lim n^((-1)^n) as n->infinity
45.
\(a_n = 1 + n \sin \frac{n \pi}{2} \)
46.
\(a_n = \frac{1}{n - 10.2} \)
