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a fost răspuns

1/2+1/6+1/12+1/20+1/30+...+1/x(x+1)=2011/2012,unde x∈Q

Răspuns :

Dariutza09
1/2+1/6+1/12+1/20+1/30+...+1/x(x+1)=2011/2012(=)1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...+  1/x(x+1)=2011/2012(=)1-1/2+1/2-1/3+1/3-1/4+1/4-1/5-1/6+...+1/x-1/x+1=2011/2012(=)       1-1/x+1=2011/2012(=)x-1/x+1=2011/2012(=)x/x+1=2011/2012(=)x=2011