Question

Folosind proprietatile adunarii numerelor rationale pozitive, calculati: (2006/2007+....+2/3+1/2)+1/2+1/3+....+1/2006+1/2007).

Answer 1

(2006/2007+....+2/3+1/2)+1/2+1/3+....+1/2006+1/2007)=
observam ca daca ii grupam cate 2:
2006/2007+1/2007=2007/2007=1
...
2/3+1/3=3/3=1
1/2+1/2=2/2=1
nr termeni de 1  = 2006
=1*2006=2006