Consider the sequences an=(n^2)/(n-1) adn bn=(-n^2)/(n-1). Since liman=∞

n->∞ and limbn=-∞, the sequences are divergent. Their sum, however, is n->∞ an+bn=((n^2)/(n-1)-(n^2)/(n-1))=0. Therefore, lim(an+bn)=0 so the sum is n->∞ convergent.

n->∞ and limbn=-∞, the sequences are divergent. Their sum, however, is n->∞ an+bn=((n^2)/(n-1)-(n^2)/(n-1))=0. Therefore, lim(an+bn)=0 so the sum is n->∞ convergent.