Question

Calculeaza .
a)2000pe34-(1pe34+2pe34+3pe34+4pe34.......+50pe34)=
b)2013pe2010 -5pe2010-10pe2010-15pe2010....-120pe2010=
c)100pe73+1pe73+2pe73+3pe73+.......++100pe73=
d)400pe81-399pe81+398pe81-397pe81+.......+2pe81-1pe81=
Sa fie si rezolvarea.

Answer 1

a)2000/34-(1/34+2/34+3/34+4/34.......+50/34)=
=2000/34-1/34(1+2+3+4+.......+50)=
=2000/34-1/34×50×51/2=
=2000/34-1/2×25×3=
=2000/17-1275/34=
=725/34

b)2013/2010 -5/2010-10/2010-15/2010....-120/2010=
=2013/2010 -5/2010(1+2+3+....+24)=
=2013/2010 -5/2010×24×25/2=
=2013/2010 -1500/2010=
=2013/2010 -1500/2010=
=513/2010=
=171/670

c)100/73+1/73+2/73+3/73+.......+100/73=
=100/73+1/73(1+2+3+.......+100)=
=100/73+1/73×100×101/2=
=100/73+1/73×50×101=
=100/73+5050/73=
=5150/73

d)400/81-399/81+398/81-397/81+.......+2/81-1/81=
=(400/81-399/81)+(398/81-397/81)+.......+(2/81-1/81)=
=1/81+1/81+....+1/81=
=200/81