Question

1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+...+(1/80+2/80+...79/80)
va rog 
eu am inteles ca e o formula

Answer 1

1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+...+(1/80+2/80+...79/80)=
=1/2+3/3+6/4+10/5+...+79(79+1)/2/80=
=0,5+1+1,5+2+.....39,5=
=(0,5+1,5+2,5....+39,5)+(1+2+3....+39)=800+780=1580
aici am calculat separat cele doua paranteze
(0,5+1,5+2,5....+39,5)=0,5(1+3+5+...79)=0,5(39x40+40)=800
(1+2+3....+39)=39(39+1)/2=39x20=780