EngStudent
New member
- Joined
- Nov 11, 2018
- Messages
- 3
Hello! New member here! I just have a quick question on a problem I have.
. . . . .\(\displaystyle \displaystyle \sum_{n=1}^{\infty}\, (-1)^{n+1}\, \left(\dfrac{n^2}{n^3\, +\, 1}\right)\)
For this problem, I used the alternating series test. Bn = n^2/(n^3+1). I showed that the limit as n approaches infinity to be 0 (2/6n = 0). Now, I just need to show that bn is decreasing. I used the first derivative test and got -x^4+2x/(x^3+1)^2. What do I do after that to show bn is decreasing or not decreasing? Thank you.
. . . . .\(\displaystyle \displaystyle \sum_{n=1}^{\infty}\, (-1)^{n+1}\, \left(\dfrac{n^2}{n^3\, +\, 1}\right)\)
For this problem, I used the alternating series test. Bn = n^2/(n^3+1). I showed that the limit as n approaches infinity to be 0 (2/6n = 0). Now, I just need to show that bn is decreasing. I used the first derivative test and got -x^4+2x/(x^3+1)^2. What do I do after that to show bn is decreasing or not decreasing? Thank you.
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