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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