Question

Arata ca numarul: a=0,5×1+0,5×3+0,5×5...+0,5×1999 este numar natural.
AJUTOOR VA ROG

Answer 1

   
[tex]\displaystyle \bf\\ a=0,5\times1+0,5\times3+0,5\times5+\cdots+0,5\times1999\\ ~~~~~~~~_\texttt{\bf Dam factor comun pe 0,5.}\\ a=0,5(1+3+5+\cdots+1999)\\ ~~~~~~~~_\texttt{\bf Calculam numarul de termeni ai sirului.}\\\\ n = \frac{1999-1}{2}+1= \frac{1998}{2}+1=999+1=1000 ~\texttt{ de termeni}\\\\ a = 0,5 \times\frac{1000(1999+1)}{2} =0,5\times \frac{1000\times2000}{2}=\\\\ =0,5\times 1000\times 1000 =500 \times 1000 = \boxed{\bf 500\:000\in N}[/tex]