Question

1/x(x+1)+1/(x+1)(x+2)+.........+1/(x+99)(x+100)=1/9

Answer 1

fractia 1/x(x+1)=1/x -1/(x+1)
1/(x+1)(x+2)=1/(x+1) -1/(x+2)
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.1/(x+99)(x+100)=1/(x+99)-1/(x+100)
daca vezi ai sa poti face simplificari si vei ramine cu1/X -1/(x+100)=1/9
x(x+100)=1/9 de aici te descurci