Are you ready for limits? Just for starters, take this expression
Now, use your calculator and substitute for 'n'.
n = 1 gives 2
n = 2 gives 2.25
n = 4 gives 2.44140625
n = 8 gives 2.565784514
n = 16 gives 2.6379284974
Care to guess where this is headed?
That's an nice parlor trick, but it doesn't say where it comes from. There are many stories about such discoveries. Just trying to solve a problem and it turns up. You left of .