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?Which of the following inequalities can be used to show that \(\sum_{n=1}^{\infty} n
Chapter 10, Problem 6(choose chapter or problem)
Which of the following inequalities can be used to show that \(\sum_{n=1}^{\infty} n /\left(n^{2}+1\right)\) diverges?
(a)\(\frac{n}{n^{2+1}} \geq \frac{1}{n^{2}+1}\) (b) \(\frac{n}{n^{2+1}} \leq \frac{1}{n}\)
(c) \(\frac{n}{n^{2+1}} \geq \frac{1}{2 n}\)
Equation Transcription:
Text Transcription:
sum _n=1^infinity n/(n^2 + 1)
n/n^2 + 1 > or = 1/n^2 + 1
n/n^2 + 1 < or = 1/n
n/n^2 + 1 > or = 1/2n
Questions & Answers
QUESTION:
Which of the following inequalities can be used to show that \(\sum_{n=1}^{\infty} n /\left(n^{2}+1\right)\) diverges?
(a)\(\frac{n}{n^{2+1}} \geq \frac{1}{n^{2}+1}\) (b) \(\frac{n}{n^{2+1}} \leq \frac{1}{n}\)
(c) \(\frac{n}{n^{2+1}} \geq \frac{1}{2 n}\)
Equation Transcription:
Text Transcription:
sum _n=1^infinity n/(n^2 + 1)
n/n^2 + 1 > or = 1/n^2 + 1
n/n^2 + 1 < or = 1/n
n/n^2 + 1 > or = 1/2n
ANSWER:
Step 1 of 3
(a) 
We cannot compare a given series with a known convergent series to prove its divergence.