Question

va rog frumos sa ma ajutati. Dau coroana.

Answer 1

1.

1-1/2+(1-5/(2*3))+(1-11/(3*4))+(1-19/(4*5))+...+(1-109/(10*11))=

=1/2+1/(2*3)+1/(3*4)+1/(4*5)+....+1/(10*11)=

=1/2+(3-2)/2*3+(4-3)/(3*4)+(5-4)/(4*5)+...+(11-10)/(10*11)=

=1/2+3/(2*3)-2/(2*3)+4/(3*4)-3/(3*4)+5/(4*5)-4/(4*5)+...+11/(10*11)-10/(10*11)=

=1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10+1/10-1/11=

=1-1/11=10/11

pentru ca -1/3+1/3=0,-1/4+1/4=0, -1/5+1/5=0 ... -1/10+1/10=0 si tot asa

2.

x÷12=a rest 10

x÷15=b rest 13

x÷18=c rest 16

x=12a+10=15b+13=18c+16

din prima egalitate→a=(5b+1)/4

din a doua→c=(5b-1)/6

numarul mai mare ca 900→b>60

a si c sunt naturale →b este impar

prin incercari →b=71

a=89,c=59

x=71*15+13=1078

3 .

y=2x

z=x+60

x+y+z=360

x+2x+x+60=360

4x=300→x=75°,y=150°,z=135°