Textbook Section 11.3 Question 23 Solutions
Question
Determine whether the series is convergent or divergent.
We use the Integral Test here which is:
-
If \(\int_2^\infty f(x) \, dx\) convergent, then \(\sum_{n=2}^{\infty} a_n\) is convergent.
-
If \(\int_2^\infty f(x) \, dx\) convergent, then \(\sum_{n=2}^{\infty} a_n\) is divergent.
Then you basically take the \(\lim_{m \to \infty} \int_2^m f(x) \, dx\) which in this case is \(\frac{1}{n \ln n}\).
You proceed to take the integral with U-Substitution and then finally taking the limit.
Since the limit does not equal to 0, it diverges which is the final answer.
Solutions
