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While writing a proof that included expansion of $(\sqrt{n} + 1)^8$ in which I know the first term has to be $n^4$, is it acceptable to write something like $(n^4 +...... + 1)$ if the $n^4$ is the only thing I really need to move progress further in the proof?

hello
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    Without more context, yes... – fosho Feb 01 '16 at 20:47
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    That would be generally acceptable as long as you give a rationale, for example using the binomial expansion .... Maybe also fix that 8 at the end while at it. – dxiv Feb 01 '16 at 20:49
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    The $+8$ at the end should be $+1$. If you want to draw attention to the fact that all terms are smaller you could write $n^4+o(n^4)$ – Ross Millikan Feb 01 '16 at 20:49
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    The next term is $8n^{7/2}$ – Henry Feb 01 '16 at 20:49
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    It's probably a bad idea, it looks like short for $n^4+n^3+n^2+n+1$. Why not just say "Let $(\sqrt n+1)^8=n^4+a$ for some $a$" and then you can just use $a$ unambiguously. – Gregory Grant Feb 01 '16 at 20:53

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Yeah, that's fine. Remember that you're allowed to use words in proofs; feel free to use as many as necessary in order to be clear. Maybe the following would be a good example:

Consider the binomial expansion of $(\sqrt{n} + 1)^8$, where the first term is $n^4$. So take $(n^4 + \ldots + 1)$ and (...your next steps here)

Newb
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