Question

cat este
1+3+5+.......+2005

Answer 1

1+3+5+....+2005
2n-1=2005
2n=2005+1
2n=2006
n=2006:2
n=1003
n^2=1003^2=1006009
Am aplicat formula generala pentru suma de numere naturale impare:
1+3+5+.....+2n-1=n^2
In caz ca vrei o demonstratie:
1+3+5+......+(2n-1)=(2*0+1)+(2*1+1)+(2*2+1)+.....+[2(n-1)+1]=
=1+1+1+.......+1+2(0+1+2+3+......+n-1)=n+2(n-1)n:2=n+n(n-1)=
=n[1+(n-1)]=n*n=n^2