Return to Answer

It can be related to the simpler $$\frac{13e^2}{3}\approx 2^5$$

because $$ \frac{3}{e^2} \approx \frac{1663}{2^{12}} = \frac{13}{2^5}-\frac{1}{2^{12}}$$

Further decomposition into alternating sign bits is $$\frac{1663}{2^{12}} = \frac{1}{2}-\frac{1}{2^3}+\frac{1}{2^5}-\frac{1}{2^{12}}$$

It can be related to the simpler $$\frac{13e^2}{3}\approx 2^5$$

because $$ \frac{3}{e^2} \approx \frac{1663}{2^{12}} = \frac{13·2^7-1}{2^{12}}= \frac{13}{2^5}-\frac{1}{2^{12}}$$

Further decomposition into alternating sign bits is $$\frac{1663}{2^{12}} = \frac{1}{2}-\frac{1}{2^3}+\frac{1}{2^5}-\frac{1}{2^{12}}$$

It can be related to the simpler $$\frac{13e^2}{3}\approx 2^5$$

because $$ \frac{3}{e^2} \approx \frac{1663}{2^{12}} = \frac{13}{2^5}-\frac{1}{2^{12}}$$

Further decomposition results in alternating sign unit fractions. $$\frac{1663}{2^{12}} = \frac{1}{2}-\frac{1}{2^3}+\frac{1}{2^5}-\frac{1}{2^{12}}$$

It can be related to the simpler $$\frac{13e^2}{3}\approx 2^5$$

because $$ \frac{3}{e^2} \approx \frac{1663}{2^{12}} = \frac{13}{2^5}-\frac{1}{2^{12}}$$

Further decomposition into alternating sign bits is $$\frac{1663}{2^{12}} = \frac{1}{2}-\frac{1}{2^3}+\frac{1}{2^5}-\frac{1}{2^{12}}$$

It can be related to the simpler $$\frac{13e^2}{3}\approx 2^5$$

because $$ \frac{3}{e^2} \approx \frac{1663}{2^{12}} = \frac{13}{2^5}-\frac{1}{2^{12}}$$

It can be related to the simpler $$\frac{13e^2}{3}\approx 2^5$$

because $$ \frac{3}{e^2} \approx \frac{1663}{2^{12}} = \frac{13}{2^5}-\frac{1}{2^{12}}$$

Further decomposition results in alternating sign unit fractions. $$\frac{1663}{2^{12}} = \frac{1}{2}-\frac{1}{2^3}+\frac{1}{2^5}-\frac{1}{2^{12}}$$