You can use the fact that exp(x+y) = exp(x)exp(y) (school A level?) and induction to show exp(5) = exp(1)^5 = exp(2)^2*exp(1) == exp(2)*exp(2)*exp(1)In order to get two places accuracy I need to take e = 2.71828 and then compute by hand the desired quantity. This can be done long hand. Any less digits will not give the desired result.So, I have to calculate some terms; the fewer the better. So, about 1 minute per computation + a minute for slippage! Or use exp(1) * ... * exp(1) 5 times depending on your speed of execution. There are more opportunies for error. One step wrong and start all over again, whereas if you get exp(2) wrong you get it wrong everywhere!
Last edited by Cuchulainn
on September 20th, 2010, 10:00 pm, edited 1 time in total.