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Rezolvați ecuația x+2x+3x+...+100x=50500

Răspuns :

factor comun x
x(1+2+....100)=50500
[tex]S100= \frac{(a1+an)n}{2}= \frac{(1+100)100}{2} =5050[/tex]
5050x=50500
x=10
(1+2+3+...+100)*x=50500
([tex] \frac{100*101}{2} [/tex])*x=50500
5050*x=50500
x=[tex] \frac{50500}{5050} [/tex]
x=10