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!

1 answer

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
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