1/1*2*3=1/1*2-1/1*3
1/2*3*4=(1/2*3-1/2*4)
1/3*4*5=(1/3*4-1/3*5)
...............................................
1/98*99*100=1/98*99-1/98*100
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1/1*2*3+...1/98*99*100=(1/1*2-1/3+1/2*3-1/2*4+1/3*4-1/3*5+...+1/98*99-1/98*100=
(1/1*2+1/2*3+...+1/98*99)-(1/1*3+1/2*4+1/3*5+....+1/98*100)
Prima paranteza este egala cu 1-1/99=98/99
Paranteza 2
1/1*3=1/2*(1-1/3)
1/2*4=1/2*(1/2-1/4)
1/3*5=1/2(1/3-1/5)
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1/98*100=1/2*(1/98-1/100)
1/1*3+1/2*4+...+1/98*100=1/2(1-1/3+1/2-1/4+1/3-1/5+...+1/98-1/100)
=termenii din mijloc dupa 1/2 se reduc si in final ramane
Paranteza 2=1/2*(1+1/2-1/100)=1/2*(3/2-1/100)=1/2*(300-1)/100=299/200
In final 98/99-299/200
