Explicație pas cu pas:
a)4+8+12+...+2012
=4(1+2+3+...+503)=
[tex] = 4( \frac{503 \times 504}{2}) = \\ = 2 \times 253512 = \\ = 507024[/tex]
b)7+14+21+...+2016=
=7(1+2+3+...+288)=
[tex]7 \times \frac{288 \times 289}{2} = \\ = 7 \times 41616 = \\ = 291312[/tex]
c)3+6+9+...+2013=
=3(1+2+3+...+671)
[tex]3 \times \frac{671 \times 672}{2} = \\ = 3 \times 225456 = \\ = 676368[/tex]
d)5+10+15+...2015=
=5(1+2+3+...+403)=
[tex]5 \times \frac{403 \times 404}{2} = \\ = 5 \times 162812 = \\ = 814060[/tex]
Am folosit formula lui Gauss
[tex] \purple{1 + 2 + 3 + ... + n = \frac{n \times (n + 1)}{2} }[/tex]
