Does
∑
n
=
1
infty
1
2
log
n
converge or diverge? Choose the correct answer with the correct justification.
The series
∑
n
=
1
infty
1
2
log
n
...
diverges by direct comparison to the harmonic series.
converges by direct comparison to the harmonic series.
converges by the ratio test.
diverges by the ratio test.
converges by direct comparison to
∑
n
=
1
infty
1
2
n
.
diverges by direct comparison to
∑
n
=
1
infty
1
2
n
.
diverges by limit comparison to
∑
n
=
1
infty
1
2
n
.
converges by limit comparison to
∑
n
=
1
infty
1
2
n
.
More generally, find all values of the positive constant
a
for which the following series converges:
∑
n
=
1
infty
1
a
log
n
.
Enter your answer using interval notation.
Answer: The series converges if and only if
a
in
equation editor
.