I need to solve this: $$ \lim_{n\to\infty} \sqrt[5]{n^5+2n^4} -\sqrt[5]{n^5-n^4} $$ I am beginner in calculating limits of sequences. I would be happy if someone could show how to solve it or give me a hint so I could try to work it out by myself. Probably it's not complicated but I don't know how to get rid of this 5th roots.
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You might want to copy this. – Did Oct 15 '15 at 21:50
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I'd factor $n^5$ outside the radical, and then use the binomial series to approximate each term. – Lucian Oct 16 '15 at 20:13
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Hint: $$a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)$$ Let $a=\sqrt[5]{n^5+2n^4}$ and $b=\sqrt[5]{n^5-n^4}$.
user170231
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