Question

Sa se calculeze
(1/2007+1/2008+1/2009+....+1/2020) + (2006/2007+2007/2008+...2019/2020)

Answer 1

(1/2007+1/2008+1/2009+....+1/2020) + (2006/2007+2007/2008+...2019/2020)=

=(1+2006)/2007+(1+2007)/2008+(1+2008)/2009+......+(1+2019)/2020

=2007/2007+2008/2008+2009/2009+....+2020/2020

=1+1+1+.....+1                   (sunt 2020-2007+1=14   de 1)

=14

Answer 2

$\frac{1}{2007}+\frac{2006}{2007}+\frac{1}{2008}+\frac{2007}{2008}+\frac{1}{2009}+\frac{2008}{2009}+...+\frac{1}{2020}+\frac{2019}{2020}=$

$=\frac{2007}{2007}+\frac{2008}{2008}+\frac{2009}{2009}+...+\frac{2020}{2020}=$

$=\[\underbrace{1+1+1+...+1}_\text{de 2020-2007=14 ori} \]=$

$=14*1=$

$=\boxed{14}$