| 1 | 1 | |||
Pokaż że | =< xn <= | . | ||
| 2n−1 | 2n−2 |
| 1 | 1 | |||
zakładając że dla n zachodzi | ≤xn≤ | mamy | ||
| 2n−1 | 2n−2 |
| 1 | 1 | ||
≤xn+1+ln(xn+1+1)≤ | |||
| 2n−1 | 2n−2 |
| x | ||
mamy x≥ln(1+x)≥ | ||
| 1+x |
| 1 | 1 | ||
≤xn+1+ln(xn+1+1)≤2xn+1 ⇒ | ≤xn+1 | ||
| 2n−1 | 2n |
| 1 | xn+12+2xn+1 | ||
≥xn+1+ln(xn+1+1)≥ | |||
| 2n−2 | 1+xn+1 |
| 1 | 1 | |||
0≥xn+12+(2− | )xn+1− | |||
| 2n−2 | 2n−2 |
| 1 | 1 | 1 | ||||
Δ=(2− | )2+ | =4+ | ||||
| 2n−2 | 2n | 4n−2 |
| 1 | ||||||||||||
xn+1≤ | ≤ | ||||||||||||
| 2 | 2n−1 |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
| Kliknij po więcej przykładów | |
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