Zbadaj monotoniczność ciągu
slowly: An=(n−1)/(3n+1)
6 kwi 20:01
M:
31 gru 06:03
M:
4 wrz 16:03
Kim Shin:
| | n | | n−1 | |
an+1−an= |
| − |
| = |
| | 3n+4 | | 3n+1 | |
| | n(3n+1)−(n−1)(3n+4) | |
= |
| = |
| | (3n+1)(3n+4) | |
| | 3n2+n−(3n2+4n−3n−4) | |
= |
| = |
| | (3n+1)(3n+4) | |
=U{4}{3n+1)(2n+4)
4>0
(3n+1)(3n+4) >0 bo n∊N
Zatem ciąg rosnący
4 wrz 18:15