Question

Dati factor comun,apoi calculati: a)10+20+30+........+800 b)13+26+39+......+715 c)21=42+36+......+1890 d)101+202+303+....+909+1010+......+9898+9999

Answer 1

a) 10+20+30+....800=    factor comun 10
=10(1+2+3+....80)=
=10(80x81):2=    (am folosit suma lui gauss)
=10x6480:2=
=64800:2=32400

b)13+26+39+...715=
=13(1+2+3+...55)=
=13x(55x56):2=
=13x3080:2=
13x1540=20020

c)21+42+63+....1890=
21(1+2+3+...90)=
=21(90x91):2=
=21x8190:2=
=21x4095=85995

d)101+202+303+....909+1010+...+9898+9999=
101(1+2+3+...9)+1010(1+2+...98+99)=
101(9x10):2+1010(99x100):2=
(101x90:2)+(1010x990:2)=
101x45+1010x495=101(45+4950)=
=101x4995=504495