Question

1+2+3+....+100
---------------------
101+102+103+.....+200
Ajutor

Answer 1

   
[tex]\displaystyle\\ \frac{1+2+3+\cdots +100}{101+102+103+\cdots +200} =?\\\\ \text{Si ls numarator si la numitor avem 100 de termeni.}\\ \text{Folosim formula lui Gauss.}\\\\ \frac{1+2+3+\cdots +100}{101+102+103+\cdots +200} = \frac{ \dfrac{100(100+1)}{2}}{\dfrac{100(200+101)}{2}}= \\\\\\ = \frac{50(100+1)}{50(200+101)} = \frac{100+1}{200+101} =\boxed{\bf \frac{101}{301}}[/tex]