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Calculați x×2x+3x+...+20x


Dau coroana


Răspuns :

Se considera suma S=x+2x+3x+...+20x

S=1x+2x+3x+...+20x
S=20x+...+3x+2x+1x
---------------------------------
2S=21x+21x+...+21x
Numar termeni : (20-1)/1+1=19/1+1=19+1=20
2S=21x×20
S=21x×20/2
S=21x×10
S=210x


Sper ca t-am ajutat ! 
S=x+2x+3x+...+20x=20x×21/2=10x×21=210×


Sper ca te-am ajutat ! :)