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$\begingroup$

In the attached image, that I have found I believe there is a mistake on the first line. Could anyone else please confirm my suspicions, thanks.

That the end of the first line should instead be $\dfrac{2}{n} - \dfrac{3}{n^2}$

Thank you

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    No; $|a-b|\leq |a|-|b|$ is not necessarily true; take $a=1, b=2$.2017-02-11
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    Of course thanks for this ^^^2017-02-11

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The modulus of (-x) is x. As the user dlc commented what you posted can be written although what you yourself said is also acceptable.