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\Huge\sf \textbf{Approximating the irrational number $e$}
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\begin{align*}
e_1=\frac1{0!}+\frac1{1!}=1+1&=2\\
e_2=e_1+\frac1{2!}=e_1+\frac12&=2.5\\
e_3=e_2+\frac1{3!}=e_2+\frac16&=2.\overline{6}\\
e_4=e_3+\frac1{4!}=e_3+\frac1{24}&=2.708\overline{3}\\
e_5=e_4+\frac1{5!}=e_4+\frac1{120}&=2.71\overline{6}\\
e_6=e_5+\frac1{6!}=e_5+\frac1{720}&=2.7180\overline{5}\\
e_7=e_6+\frac1{7!}=e_6+\frac1{5040}&=2.718\overline{253968}\\
e_8=e_7+\frac1{8!}=e_7+\frac1{40320}&=2.7182787\overline{698412}\\
e_9=e_8+\frac1{9!}=e_8+\frac1{362880}&=2.718281\overline{525573192239858906}\\
e_{10}=e_9+\frac1{10!}=e_9+\frac1{3628800}&=2.71828180\overline{114638447971781305}\\
e_{11}=e_{10}+\frac1{11!}=e_{10}+\frac1{39916800}&=2.7182818\overline{261984928651595318}\\
e_{12}=e_{11}+\frac1{12!}=e_{11}+\frac1{479001600}&=2.7182818282\overline{861685639463417241195018972796750574528352306130083907}\\
e_{13}=e_{12}+\frac1{13!}=e_{12}+\frac1{6227020800}&=2.718281828\overline{446759002314557870113425668981224536780092335647891203}\\
e_{14}=e_{13}+\frac1{14!}=e_{13}+\frac1{87178291200}&=
2.71828182845\overline{822974791228759482727736695990664244632498600752569006}\\
&\phantom{\ =2.71828182845}\overline{537260505514473768442022410276378530346784315038283292}\\
&\phantom{\ =2.71828182845}\overline{251546219800188054156308124562092816061070029323997577}\\
&\phantom{\ =2.71828182845}\overline{965831934085902339870593838847807101775355743609711863}\\
&\phantom{\ =2.71828182845}\overline{680117648371616625584879553133521387489641457895426149}\\
&\phantom{\ =2.71828182845}\overline{394403362657330911299165267419235673203927172181140435}\\
&\phantom{\ =2.71828182845}\overline{108689076943045197013450981704949958918212886466854720}\\
\end{align*}
\begin{center}\tiny 
Approximating $e$ --- 
Math Poster 2009 --- math.chapman.edu
\end{center}
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