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2014-10-10T19:43:49+03:00
N=1+3+5+7+...+999=
n=1ori(1+2+...+999):2
n=1ori 999ori1000:2
n=1ori 999000:2
n=1ori 499500
n=499500
2014-10-10T19:54:24+03:00

1= 1

3 =1+2·1

5= 1+2·2

7= 1+2·3

................

999=1+2·499  ⇒ S = 1·500 + 2(1+2+3+.....+499) =   500  + 2·499·500/2 = 500·500 = 250000

S= 1   +   2  + 3+..............+499   (1)

S=499+498+497+....+3+2+1       (2)  din (1)+(2) ⇒ S+S =  2S = 500+500+.....de 499 de ori....+500= 499×500 ⇒ S=499·500÷2