Question

1/2•(2°+4°+6°+........+22°)=55°

Answer 1

   
[tex]\displaystyle\\ \frac{1}{2}\cdot (2^o+4^o+6^o+\cdots+22^o)=\\\\ =\frac{2^o+4^o+6^o+\cdots+22^o}{2}=\\\\ =\frac{2(1^o+2^o+3^o+\cdots+11^o)}{2}=~~~~~\text{(Am dat factor comun pe 2)}\\\\ =1^o+2^o+3^o+\cdots+11^o =~~~~~\text{(Am simplificat cu 2)}\\\\ = \frac{11(11+1)}{2}=\frac{11 \cdot 12}{2}=11 \cdot 6 = 66^o \\\\ \text{Daca ultimul termen ar fi fost }~20^o ~\text{ in loc de }~22^o ~\text{ atunci}\\ \text{rezultatul ar fi fost }~55^o. [/tex]

Answer 2

1/2·(2 + 4 + .. + 22) = 55

1/2·2·(1 + 2 + .. + 11) = 55

1 + 2 + .. + 11 = 55  (aplicam suma lui Gauss)

11·12/2 = 55

11·6 = 55

66 = 55 (Fals)