Question 199187
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You cannot 'solve' it in any sense of the word solve that I know.  The only way to express *[tex \Large 6e] exactly is just that: *[tex \Large 6e].  You can express a numerical approximation to as many decimal places as you like by multiplying 6 times an appropriately precise representation of *[tex \Large e].  The Windows built-in calculator gives e to more decimal places than I can conceive of a practical use, namely: 2.7182818284590452353602874713527.  But if that is insufficient for your needs you can use the following:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ e =\ \lim_{n\rightarrow\infty}\ \sum_{i=0}^n\,\frac{2n+2}{(2n+1)!}]


The larger number you select for *[tex \Large n], the closer you get.  For example *[tex \Large n = 6] gets you a nine-digit decimal approximation.


*[tex \Large e] is most assuredly irrational.  In fact, it is transcendental, meaning that it is not an algebraic number, that is, it is not the root of any polynomial equation with rational coefficients.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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