Question

Exercițiile 6b și 5d
Vă rog repede

Answer 1

5d)
1/1*2=1/1-1/2
2/2*4=1/2-1/4
3/4*7=1/4-1/7
5/7*12=1/7-1/12
7/12*19=1/12-1/19
9/19*28=1/19-1/28
se aduna si se observa ca -1/2+1/2=0   -1/4+1/4=0  si asa mai departe
raman doar 1/1 si -1/28
1/1*2+2/2*4+3/4*7+5/7*12+7/12*19+9/19*28=1/1-1/28=(28-1)/28=27/28

6b
1/2=1/1*2=1/1-1/2
1/6=1/2*3=1/2-1/3
1/12=1/3*4=1/3-1/4
1/20=1/4*5=1/4-1/5
1/30=1/5*6=1/5-1/6
.....
1/420=1/20*21=1/20-1/21

1/2+1/6+1/12+1/20+1/30+.....1/420=
=1/1-1/21=(21-1)/21=20/21