| 1 | 1 | 1 | 1 | ||||
+ | + | + ... + | = ? | ||||
| 2√1+1√2 | 3√2+2√3 | 4√3+3√4 | 16√15+15√16 |
| 1 | 1 | ||
= | = | ||
| (k+1)√k+k√k+1 | √k√k+1(√k+1+√k) |
| 1 | √k+1−√k | ||
* | = | ||
| √k√k+1(√k+1+√k) | √k+1−√k |
| √k+1−√k | 1 | 1 | |||
=( | − | ) | |||
| √k√k+1 | √k | √k+1 |
| 1 | 1 | 1 | 1 | 1 | 1 | |||||||
( | − | )+( | − | )+...+ | − | ) | ||||||
| √1 | √2 | √2 | √3 | √15 | √16 |
| 1 | ||
=1− | =1−1/4=3/4 | |
| √16 |
mam nadzieję, że uda mi się to przeanalizować i zrozumieć