wykaz ze dowolna n>=1 spelnia rownanie
agravka: Wykaz ze dla dowolnej liczby naturalnej n≥1 spelniona jest nierownosc
1/(2*4)+1/(4*6)+1/(6*8)+...+1/(2n(2n+2))<1/4
9 sty 09:38
irena_1:
1 | | 1 | | 1 | | 1 | |
| + |
| + |
| +...+ |
| = |
2*4 | | 4*6 | | 6*8 | | 2n(2n+2) | |
| 1 | | 1 | | 1 | | 1 | |
= |
| *( |
| + |
| +...+ |
| )= |
| 4 | | 1*2 | | 2*3 | | n(n+1) | |
| 1 | | 1 | | 1 | | n+1−1 | | 1 | | n | | 1 | | 1 | |
= |
| *(1− |
| )= |
| * |
| = |
| * |
| < |
| *1= |
| |
| 4 | | n+1 | | 4 | | n+1 | | 4 | | n+1 | | 4 | | 4 | |
9 sty 10:58