działania na liczbach
Kinga03: Czy ktoś pomoże z uproszczeniem tego wyrażenia:
1+(2+1)*(22 +1)*(24 +1)*(28 +1)*(216+1)*(232 +1)*(264 +1)
13 lip 18:29
Szkolniak: | 1+(2+1)(22+1)(24+1)(28+1)(216+1)(232+1)(264+1) | |
| *(22−1)= |
| 22−1 | |
| | (22−1)+(3)(22−1)(22+1)(24+1)(28+1)(216+1)(232+1)(264+1) | |
= |
| = |
| | 22−1 | |
| | (22−1)+(3)(24−1)(24+1)(28+1)(216+1)(232+1)(264+1) | |
= |
| = |
| | 22−1 | |
| | (22−1)+(3)(28−1)(28+1)(216+1)(232+1)(264+1) | |
= |
| =... |
| | 22−1 | |
| | 3+3(264−1)(264+1) | |
...= |
| = |
| | 3 | |
=1+2
128−1=2
128
13 lip 18:38
jc:
2+1=(2+1)(2−1)=22−1
(2+1)(22+1)=(22−1)(22+1)=24−1
(2+1)(222+1)(24+1)=(24−1)(24+1)=28−1
itd.
Dlatego rozpatrywane wyrażenie = 2128
13 lip 18:38
kerajs:
Lekka modyfikacja rozwiązania Szkolniaka:
| | (21−1) * (21+1)*(22 +1)*(24 +1)*(28 +1)*(216+1)*(232 +1)*(264 +1) | |
1+ |
| = |
| | 21−1 | |
=1+(2
2−1)*(2
2 +1)*(2
4 +1)*(2
8 +1)*(2
16+1)*(2
32 +1)*(2
64 +1)=
1+(2
4−1)*(2
4 +1)*(2
8 +1)*(2
16+1)*(2
32 +1)*(2
64 +1)=...=1+2
128−1
13 lip 18:50