3+5+7+....+(2n+1)=n(n+2)
se rezolva cu ajutorul sumelor Gauss
1 + 2 + 3 + .......+ n =[n (n+1)}:2
3 + 5 + 7 + ....+ (2n + 1)
= 1 + 2 + 3 +....+ (2n+1) + ( 2n +2) - 1 - 2 [1 + 2 + 3 +.....+n + (n + 1)]
= [(2n + 2)(2n + 3)]:2 -1 - 2[(n + 1)(n + 2)]:2
= (n + 1)(2n + 3) -1 - (n + 1) ( n + 2)
= ( n + 1)( 2n +3 -n - n) -1
= (n + 1)²-1
= n² +2n
= n(n+2)
