Question

10+20+30+...+800;





13+26+39+...+715;





21+42+36+...+1890;





101+202+303+...+909+1010+...+9898+9999;




4 sume ale lui gaoss

​

Answer 1

Răspuns:

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

Sper ca te-am ajutat!  :D

Answer 2

Răspuns:

10+20+30+...+800=10(1+2+3+..+80)=10((80x81):2)==10x3240=32400

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

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

Explicație pas cu pas: