Question

cum se calculeaza 7+11+15+....+999=?

Answer 1

 7+11+15+....+999 = 3+7+11+15+...+999 - 3 =

= (1+2)+(3+4)+(5+6) +(7+8)+...+(499 + 500) - 3  =            (999:2 = 499 rest 1)

=1+2+3+4+...+500 - 3=

Acum folosim formula: $1+2+3+4+...+n = \frac{n\cdot(n+1)}{2}$ si avem:

 $=\frac{500\cdot501}{2}-3 = 250\cdot 501 -3 = 125250 - 3$ = 125247

Answer 2

S=7+11+15+...+999
7=4*1+3
11=4*2+3
15=4*3+3
...
999=4*249+3
S=4(1+2+3+...+249)+3*249
S=4*249*125+3*249
S=249*500+3*249
S=249*503