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simplificati fractia: F=1001+1002+...+2000 supra 2001+2002+...+3000 urgentttt

Răspuns :

Se aplica formula lui Gauss: 1+2+...+n=n(n+1)/2
1001+1002+...+2000=(1+2+...+2000)-(1+2+...+1000)=
=2000x2001/2 -1000x1001/2=1000x2001-500x1001=
=2001000-500500=1500500
2001+2002+...+3000=(1+2+...+3000)-(1+2+...+2000)=
3000x3001/2 -2000x2001/2=1500x3001-1000x2001=
=4501500-2001000=2500500
F=1500500/2500500=15005/25005=3001/5001
F=3001/5001

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