Question

De ce $\frac{1}{1*2}+ \frac{1}{2*3}+ \frac{1}{3*4}+...+ \frac{1}{2014*2015}=1- \frac{1}{2015}$?

Answer 1

numere consecutive  1 / n · ( n +1 )   = 1  / n   - 1 / ( n +1 ) 
fiecare termen devine  o scadere 
= [ 1 /1  - 1 /2 ] + [1 /2 - 1 /3 ] + [1 /3 - 1 /4 ] + ... + [ 1 /2014 -  1 /2015 ]
 raman primul si ultimul termen 
= 1 /1   - 1 /2015  , adevarat

Answer 2

[1/1-1/2]+[1/2-1/3]+[1/3-1/4]+....+[1/2014-1/2015]
⇒1/1-1/2015=1-1/2015⇒adevarat⇒se reduce termenii cu aceeasi valoare numerica;