Somme des premiers termes 1/3 1/3
Cas d’une suite arithmétique de 1er terme u1 d’

S = u1 + u2 + u3 + …. + un-3 + un-2+ un-1+ un S = un + un-1+ un-2 + …. + u4 + u3 + u2 + u1
un-3 + u4 = u1 + (n-4)r + u1 + 3r = 2u1 + (n-1)r un-1 + u2 = u1 + (n-2)r + u1 + r = 2u1 + (n-1)r un+ u1 = u1 + (n-1)r + u1 = 2u1 + (n-1)r

Donc : un+ u1 = un-1 + u2 = un-3 + u4 =…= 2u1 + (n-1)r