Question

$\frac{1}{10*20}+ \frac{1}{20*30}+ \frac{1}{30*40}+...+ \frac{1}{990*1000}=$


[/tex][tex] \frac{1}{9*22}+ \frac{1}{18*33}+ \frac{1}{27*44}+...+ \frac{1}{891*1100} =

[/tex]

mersi :)

Answer 1

1 /100 · [ 1 /1·2 + 1 / 2·3 + 1 /3·4 + ... + 1 / 99 · 100 ] = 
 = 1 / 9 ·11  · [ 1 /1·2  + 1 / 2· 3 + 1 / 3 ·4 + ... + 1 / 99 · 100 ] 
simplificam parantezele  
 1 / 100 = [/text ] 1 / 99 
                   ↓
                    ?