Question

Calculati :

1 supra 1*2 - 1 supra 2*3 + 1 supra 3*4 +.............+ 1 supra 99*100

Mersi .

Answer 1

se foloseste formula ,, 1 / [k(k+1)] = 1/k - 1/(k+1) "

... = 1/1 - 1/2 + 1/2 - 1/3 +1/3 -1/4 + ... +1/98 - 1/99+1/99 - 1/100 =
    = 1/1 - 1/100 = (100-1)/100 = 99/100 ;
   

Answer 2

1/1*2=1/1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
......
1/99*100=1/99-1/100

se aduna toate fractiile

 1/1 - 1/2 + 1/2 - 1/3 +1/3 -1/4 + ... +1/98 - 1/99+1/99 - 1/100
si dupa reducerea termenilor asemenea mai raman:

1/1-1/100
(100-1)/100=99/100