Question

(x +1) +(x +2)+ (x +3)+ ...+ (x +100)=99x+5728
va rog dau coroana primului raspuns corect

Answer 1

(x +1) +(x +2)+ (x +3)+ ...+ (x +100)=99x+5728
100x+(1+2+3+....+100)=99x+5728
x=5728-100*101:2
x=5728-5050
x=678

Answer 2

$(x+1)+(x+2)+(x+3)+ ... +(x+100) = 99x+5728$

Partea stanga a ecuatiei se poate aranja astfel:

100x+(1+2+3+ ... +100) =99x+5728

Aplicam suma lui Gauss:

$100x+\dfrac{100\cdot101}{2}=99x+5728 \Longrightarrow 100x+50\cdot101 = 99x+5728$

$100x +5050 =99x+5728 \Longrightarrow 100x-99x=5728- 5050$