Mathematics

Problem

Consider the series

\displaystyle\sum_{n=1}^{\infty}\frac{1}{\sqrt{n}}

. Using only the

n

th-term test, which conclusion can be drawn? a) The series converges by the

p

-series test since

p=\tfrac12>1

. b) The series converges because its terms decrease to zero sufficiently fast. c) The

n

th-term test is inconclusive because

\displaystyle\lim_{n\to\infty}\frac{1}{\sqrt{n}}=0

. d) The

n

th-term test cannot be applied here because the terms are not alternating.