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x+2x+3x+.....100x=1000

Răspuns :

x+2x+3x+.......+100x=[100*(100+1):2]x=(50*101)x=5050x
5050x=1000
x=1000:5050
x=20/101
 [tex]x(\underbrace{1+2+3+...+100}_{=\frac{100*101}{2}})=1000\\ x=1000\,:\,(50\cdot101)=1000\,:\,5050=0,(1980)[/tex]