Question

Calculati folosind factorul comun:
a)4+8+12+...+2012
b)7+14+21+...+2016
c)3+6+9+...+2013
d)5+10+15+...2015
Va rog sa le rezolvati complet adc nu cateva pt ca am vazut ca uni fac decat vreo 2-3
dau coroana
va rog frumos din suflet am mare nevoie

va rog frumossssssssssssssssssssssssssss

Answer 1

Explicație pas cu pas:

a)4+8+12+...+2012

=4(1+2+3+...+503)=

$= 4( \frac{503 \times 504}{2}) = \\ = 2 \times 253512 = \\ = 507024$

b)7+14+21+...+2016=

=7(1+2+3+...+288)=

$7 \times \frac{288 \times 289}{2} = \\ = 7 \times 41616 = \\ = 291312$

c)3+6+9+...+2013=

=3(1+2+3+...+671)

$3 \times \frac{671 \times 672}{2} = \\ = 3 \times 225456 = \\ = 676368$

d)5+10+15+...2015=

=5(1+2+3+...+403)=

$5 \times \frac{403 \times 404}{2} = \\ = 5 \times 162812 = \\ = 814060$

Am folosit formula lui Gauss

$\purple{1 + 2 + 3 + ... + n = \frac{n \times (n + 1)}{2} }$