Răspuns:
1/1*3=1/2(1-1/3)
1/2*4=1/2(1-1/2)
1/3*5=1/2(1/3-1/5)
1/4*6=1/2(1/2-1/3)
_____________Le adui
1/1*3+1/2*4+1/3*5+1/4*6=1/2(1-1/3+1-1/2+1/3-1/5+1/2-1/3)= reduci termenii asemenea
=1/2(1+1-1/5-1/3)=1/2*(4/5+2/3)=1/2(4*3/15+2*5/15)=1/2(12+10)/15=
1/2*22/15=
11/15
Explicație pas cu pas:
Răspuns:
Explicație pas cu pas:
[tex]Formula~~~\dfrac{1}{n*(n+k)}=\dfrac{1}{k}*(\dfrac{1}{n}- \dfrac{1}{n+k})\\[/tex]
La acest exercitiu, k=2
[tex]\dfrac{1}{1*3}+\dfrac{1}{2*4}+\dfrac{1}{3*5}+\dfrac{1}{4*6}=\dfrac{1}{2}*(\dfrac{1}{1}-\dfrac{1}{3})+ \dfrac{1}{2}*(\dfrac{1}{2}-\dfrac{1}{4})+\dfrac{1}{2}*(\dfrac{1}{3}-\dfrac{1}{5})+\dfrac{1}{2}*(\dfrac{1}{4}-\dfrac{1}{6})=\dfrac{1}{2}*( \dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}-\dfrac{1}{6})=\dfrac{1}{2}*( \dfrac{1}{1} +\dfrac{1}{2}-\dfrac{1}{5}-\dfrac{1}{6})=\dfrac{1}{2}*\dfrac{30+15-6-5}{30}=\dfrac{1}{2}*\dfrac{34}{30}=\dfrac{17}{30}[/tex]
