Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.
<h3>How do we verify if a sequence converges of diverges?</h3>
Suppose an infinity sequence defined by:
![\sum_{k = 0}^{\infty} f(k)](https://tex.z-dn.net/?f=%5Csum_%7Bk%20%3D%200%7D%5E%7B%5Cinfty%7D%20f%28k%29)
Then we have to calculate the following limit:
![\lim_{k \rightarrow \infty} f(k)](https://tex.z-dn.net/?f=%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20f%28k%29)
If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.
In this problem, the function that defines the sequence is:
![f(k) = \frac{k^3}{k^4 + 10}](https://tex.z-dn.net/?f=f%28k%29%20%3D%20%5Cfrac%7Bk%5E3%7D%7Bk%5E4%20%2B%2010%7D)
Hence the limit is:
![\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0](https://tex.z-dn.net/?f=%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20f%28k%29%20%3D%20%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7Bk%5E3%7D%7Bk%5E4%20%2B%2010%7D%20%3D%20%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7Bk%5E3%7D%7Bk%5E4%7D%20%3D%20%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Cinfty%7D%20%3D%200)
Hence, the infinite sequence converges, as the limit does not go to infinity.
More can be learned about convergent sequences at brainly.com/question/6635869
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To get you answer multiply .3 and 2.7
Answer: 517
Step-by-step explanation: