Asked by Laura
I need to find if the summation of (n^4)/(n^10 + 1) is convergent or divergent from n=1 to infinity.
I tried splitting it up into two sums, one being 1/n^6, which would be convergent because p=6>1, and then the other being n^4, but I'm not sure how to know if this is convergent or divergent.
I know the answer is convergent for the entire series because I first tried to answer divergent, but I don't know why it is convergent. Thanks!
I tried splitting it up into two sums, one being 1/n^6, which would be convergent because p=6>1, and then the other being n^4, but I'm not sure how to know if this is convergent or divergent.
I know the answer is convergent for the entire series because I first tried to answer divergent, but I don't know why it is convergent. Thanks!
Answers
Answered by
Steve
it is clearly convergent, because
(n^4)/(n^10 + 1) < n^4/n^10 = 1/n^6
and 1/n^p is convergent for p>1
(n^4)/(n^10 + 1) < n^4/n^10 = 1/n^6
and 1/n^p is convergent for p>1
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.