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determinati nr natural x,daca:4+8+12+.......396=200x

Răspuns :

4+8+12+...+396=200x  l:4
1+2+3+...+99=50x
[tex] \frac{99x100}{2} = \frac{9900}{2} =4950[/tex]
4950=50x
x=[tex] \frac{4950}{50} =99[/tex]
4+8+12+...+396=200x  l:4
4×(1+2+3+........+99)=200x
(1+2+3+........+99) suma Gauss cu formula de calcul S=[n(n+1)]:2=(99×100):2=4950

4×4950=200x
x=(4950×4):200
x=99