Question

afla valoarea lui x : 2+4+6+...+98+x=1+2+3+4+5+...99

Answer 1

Suma lui Gauss:
$1+2+3+...+n= \frac{n(n+1)}{2}$

Avem:

[tex]2+4+6+...+98+x=1+2+3+...+99 \\ 2(1+2+3+...+49)+x= \frac{99(99+1)}{2} \\ 2* \frac{49(49+1)}{2}+x =99*50 \\ 2*49*25+x=4950 \\ 2450+x=4950 \\ x=4950-2450 \\ x=2500[/tex]