Mathematics

Problem

Consider the series

\displaystyle \sum_{n=4}^{\infty}\frac{5n^{2}+1}{n^{3}}

. Which statement about its convergence is correct? a) The series converges because the

n^{3}

in the denominator overpowers the numerator. b) The information given is insufficient; another convergence test is required to draw a conclusion. c) The series diverges because, for large

n

, the terms behave like

\tfrac{1}{n}

, the harmonic series. d) The series converges by comparison with

\displaystyle \sum\frac{1}{n^{3}}

, a

p

-series with

p=3

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