Casio hand calculator vs Mathematica at (1+1/n)^n The CASIO fx-7400G calculator is very quick at doing $(1+1/1000000)^{1000000}$, giving an output of $2.718280469$.
Mathematica (v7) takes over a minute, running on an Intel Core2 Duo processor, and its output is this:

With $n=10000000$, my patience ran out. The calculator is quick again with an output of $2.718281693$.
Does anybody know why this happens?
 A: General purpose computer algebra systems, unlike most calculators, are able to perform both exact/symbolic computations (e.g. exact integer arithmetic) in addition to approximate numerical computations (e.g. floating point). Thus when you present the problem in exact terms - as you do above - they will preserve that form - so as not to lose any information. Thus your problem will be interpreted as a computation in exact rational arithmetic, i.e. raising a rational number to an integer power. If instead you desire a real approximation of the result then you must explicitly specify such, e.g. using N[...] in Mma. This is but one of the many complexities that arise when one passes from special-purpose computation systems (e.g. calculators) to general purpose computer algebra systems (speaking as one who has often tried to tackle less trivial such complexities while working as a developer of the Macsyma computer algebra system). 
A: I think your calculator might use $$ a^b = \exp(b\ln a)$$ together with precalculated $\exp$ and $\ln$ tables to speed things up.
I know I would =)
