Răspuns:
Explicație pas cu pas:
x-2x+3x-4x+.....+99x-100x=500
Le grupam cate doua x-2x=-x ; 3x-4x=-x .......99x-100x=-x de 50 de ori
50(-x)=500 ⇒x=-100
x-2x+3x-4x+.. .+99x-100x=500
x(1-2+3-4+...+99-100)=500
x[1+3+5+...+99)-2(1+2+3+...+50)]=500
99=2n-1
n=100/2=50
prima sumă=n²=50²
a doua sumă= 50×51/2=50×51/2
50²-2×(50×51/2)=50²-50×51=50(50-51)=-50
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Răspuns:
Explicație pas cu pas:
x-2x+3x-4x+.....+99x-100x=500
Le grupam cate doua x-2x=-x ; 3x-4x=-x .......99x-100x=-x de 50 de ori
50(-x)=500 ⇒x=-100
x-2x+3x-4x+.. .+99x-100x=500
x(1-2+3-4+...+99-100)=500
x[1+3+5+...+99)-2(1+2+3+...+50)]=500
99=2n-1
n=100/2=50
prima sumă=n²=50²
a doua sumă= 50×51/2=50×51/2
50²-2×(50×51/2)=50²-50×51=50(50-51)=-50
x=500/(-50)=-10