Some simple series

$\dfrac{1}{1-x}$
1-x and inv
$\dfrac{1}{1-x}=1+x+x^2+x^3+x^4+\cdots$

When $x=\fr{2}$ :
zeno series

$\dfrac{1}{1+x}$
1+x and inv

$\dfrac{1}{1-x^2}$
1o1-x2

$\dfrac{1}{1+x^2}$
1o 1pxs

$\dfrac{1}{(1-x)^2}$
1o 1-x 2
1o1-r sq

$\dfrac{1}{(1+x)^2}$
1o 1px 2

Sum of reciprocals of triangular numbers

$\fr{1}+\fr{3}+\fr{6}+\fr{10}+\dots=\sum\limits_{k=1}^\infty \frac{1}{\sum\limits_{n=1}^k n}= \sum \frac{2}{n(n+1)}=\sum \fr{\binom{n+1}{2}}$

recip of tri ns

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