Write down the first 50 terms of the series for e^{-x}.
Go back in time and tell Pythagoras to plug in x=2,3,4,5,6,7,8,10,...
Each of the terms is a rational number, and the each of the sums will be an extremely small rational number (numerator will be tiny compared to denominator).
Don't you think Pythagoras would be impressed and mystified?
Would he be able to come up with an explanation for this `coincidence'?
Now try the same with with x-x. That's not going to impress Pythagoras.
Each of the terms is a rational number, and the each of the sums will be an extremely small rational number (numerator will be tiny compared to denominator).
Don't you think Pythagoras would be impressed and mystified? Would he be able to come up with an explanation for this `coincidence'?
Now try the same with with x-x. That's not going to impress Pythagoras.