Question

Va rog ex 5 si 6,Helppp

Answer 1

1.
1/2+1/6+1/12+1/20+....+1/870
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
.....
1/870=1/29*30=1/29-1/30
1/2+1/6+1/12+1/20+...+1/870=
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/29-1/30=1/1-1/30=(30-1)/30=29/30


in cazul in care se repeta cartonasul 1/6
1/6+1/6+1/12+1/20+....+1/870
1/6=1/2*3=1/2-1/3
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
.....
1/870=1/29*30=1/29-1/30
1/6+1/6+1/12+1/20+...+1/870=
=1/2-1/3+1/2-1/3+1/3-1/4+1/4-1/5+...+1/29-1/30=
=1/2-1/3+1/2-1/30=
=2/2-1/3-1/30=
=(30-10-1)/30=
=19/30

100%+10%=110%
1331:110%=1210 lei

100%+10%=110%
1210:110%=1100 lei

100%+10%=110%
1100:110%=1000 lei pre initial