Question

Să se arate că
1/1*4+1/4*7+...+1/ 2005*2008=1/3(1-1/2007)

Answer 1

Notam S=1/(1*4)+1/(4*7)+...+1/(2005*2008).

1/(1*4)=1/3*(1/1-1/4)
1/(4*7)=1/3*(1/4-1/7)
1/(7*10)=1/3*(1/7-1/10)
...
1/(2002*2005)=1/3*(1/2002-1/2005)
1/(2005*2008)=1/3*(1/2005-1/2008)

Asadar S=1/3*(1/1-1/4+1/4-1/7+1/7-1/10+...+1/2002-1/2005+1/2005-1/2008)=1/3*(1-1/2008).