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1. a) 1/2+1/6+1/12+1/20+1/30+...+1/x(x+1)=2011/2012

Răspuns :

1/1×2+1/2×3+1/3×4+.....+1/×(×+1)=2-1/1×2+3-2/2×3+....+×+1-×/×(×+1)
=2/1×2-1/1×2+3/2×3-2/2×3+.....+×+1/×(×+1)-×/×(×+1)
Prin simplificari rezulta 1-1/×+1=2011/2012
Aduci la acelasi numitor si il afli pe x. Succes