Question

Se considera numarul real x astfel incat:
x=$\frac{1}{1x2}$+$\frac{1}{2x3}$+$\frac{1}{3x4}$+...+$\frac{1}{9x10}$
Aflati partea intreaga si partea fractionara a lui x.

Answer 1

1 /1· 2 =  1 /1 -  1 /2
1 /2· 3 = 1 /2 -   1 /3
1 / 3 · 4= 1 /3 -  1 /4 
...........................
1 / 9 · 10 = 1 /9  - 1 /10 
-------------------------------------
suma = 1 /1   - 1 /10  = (10 - 1) / 10  = 9 /10 = 0.9 
[0,9]= 0 
{ 0.9} = 0,9