Question

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

Answer 1

a) 10+20+30+...800 =
=10(1+2+3+....80) =
= 10(80*81)/2 =    
= 10*6480/2 =
= 64800/2 = 
= 32400

d) 13+26+39+...+715 = 
= 13(1+2+3+...55) =
= 13*(55*56)/2 =
= 13*3080/2 =
= 13*1540=
=20020

c) 21+42+63+....1890 =
= 21(1+2+3+...90)=
= 21(90*91)/2 =
= 21*8190/2 =
= 21*4095 =
=85995


d) 101+202+303+…+909+1010+…+9898+9999 = 
= 101(1+2+3+...9)+1010(1+2+...98+99) =
= 101(9*10)/2+1010(99*100)/2 =
= (101*90/2)+(1010*990/2) =
= 101*45+1010*495=101(45+4950) =
= 101*4995=
= 504495

Answer 2

suma lui Gauss 1+2+3+...+n=nx(n+1):2


10+20+30+...+800=10x(1+2+3+...+80)=10x80x81:2=32400

13+26+39+...+715=13x(1+2+3+...+55)=13x55x56:2=20020

21+42+63+...+1890=21x(1+2+3+...+90)=21x90x91:2=85995

101+202+303+...+909+1010+...+9898+9999=101x(1+2+3+...+9+10+...+98+99)=101x99x100;2=504495