User:I like pie

I am a user on AoPS, and go by the username i_like_pie. I enjoy playing soccer, programming, talking to my friends, fishing, reading, and many other things.

For Future Use

$\displaystyle\sum^{n}_{k=1}\left(\frac{1}{x}\right)^k=\frac{x^{n}-1}{x^{n}(x-1)}$

$\lim_{n\rightarrow\infty}\left(\displaystyle\sum^{n}_{k=1}\left(\frac{1}{x}\right)^k\right)=\frac{1}{x-1}$

$\left\lceil\frac{x^{n}-1}{x^{n}}\right\rceil=\frac{1}{x-1}$

$\frac{x^{n}-1}{x^{n}}<\frac{1}{x-1}$

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User:I like pie

For Future Use