Determine if the series is convergent? summation of n/(10n+3), n-->infinite Solution To check if the series converges or diverges, we\'ll have to evaluate the limit of the series. Let an = Sum n/(10n + 3) lim an = lim n/(10n + 3) lim an = lim n/n*(10 + 3/n) We\'ll simplify and we\'ll get: lim an = lim 1/(10 + 3/n) Since the limit of the fraction 3/n converges to zero, we\'ll have: lim an = 1/10 Since the value of the limit is 1/10, therefore the series converges to 1/10..