An algebra problem by Benedicto Amora Jr.

All odd numbers can be written as 2k+1, with k as an integer positive. In this case, we do a sum of all odd number from 1017 to 1030191, so we do the sum between : A=2b+1=1017 <=> A=1016/2=508 and B=2a+1=1030191 <=> B=1030190/2=51595

We sum all the terms beetween A and B with the form 2k+1 which is in fact twice the sum between A and B plus (515095+1)-(508+1). So we have just to calculate the sum of all k between A and B, equal as :

Σk[A->B]=Σk[1->A]-Σk[1->B]=132661558282,5

Σ2k[A->B]= 265323116565

Σ2k+1[A->B]=265323116565+Σ1[A->B]

Σ2k+1[A->B]=265323116565+515096-509=265323631152

1017, 1019, 1021,..............................................1030191 is a A.P. Xn = a + d(n-1) Xn= 1030191 a= 1017 d=2 n=? n =514588 SUM= n(a+Xn)/2 =514588(1017+1030191)/2 =265323631152