Question

Efectuati:

10+15+20+....+2010-9-13-17-....-1609

Answer 1

10+15+20+.....+2010-9-13-17-.......-1609 =405010-324409=80601

Rezolvare:

10+15+20+.....+2010=5(2+3+4+....+402)+5-5=5(1+2+3+...+402)-5=

=5×402×403/2-5=405010

-9-13-17-.......-1609 =

13-9=4

Nr Termeni:    (1609-9):4+1=400+1=401

=-(9+9+4+9+8-.......+9+1600)=-401×9 -4(1+2+3+....400)= =-3609-4×400×401/2=-3609-320800=-324409

10+20+30+....+2020-9-18-27-....-1818  =

=10(1+2+3+....+202)-9(1+2+3+...+202)=(202×203:2)(10-9)=101×203=20503