Question

pct b) și c),va rog repede dau coroana

Answer 1

b) $\frac{1}{1*2}+ \frac{1}{2*3} +...+ \frac{1}{2013*2014}=$
$= \frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+ \frac{1}{2013}-\frac{1}{2014}$

se simplifica si ramane $\frac{1}{1}-\frac{1}{2014} =2013/2014$

b) aduci la acelasi numitor

$\frac{n+m}{n*(n+m)} -\frac{n}{n*(n+m)}= \frac{m}{n*(n+m)}$
oricare ar fi n,m din N*