# If Σ an and Σ bn are series of positive terms and lim an/bn=0 from n to +∞ show by example that Σ an may converge and Σ bn not converge solved problems in calculus

Let a_n=\frac{1}{n^{2}} and b_n=\frac{1}{n}. \lim_{n\rightarrow +\infty}\frac{a_n}{b_n}=\lim_{n\rightarrow +\infty}\frac{1}{n}=0 but, \sum \frac{1}{n^2} converges and \sum \frac{1}{n} diverges.