Question
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
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