Question

Cum as putea sa calculez:
a) 150+151+...+2013
b)2+4+6+...+2012
c)1+3+5+7+...+2013

Va rog, ajutor!

Answer 1

Aplici Legea lui GAUSS

1+2+..+n=(n·n+1)/2

a)1+2+...+2013=2013*2014/2-(1+2+...149)=

=2027091-149*150/2

=2015916

b)2(1+2+..+1006)=

=2*1006*1007/2

=1013042

c)(2*0+1)+(2*1+1)+...+(2*1006+1)

=2(1+2+..+1006)+1007

=2*1006*1007/2+1007

=1007(1006+1)

=1007²

=1014049