Calculating e


[Prev][Next][Index][Thread]

Calculating e



I wanted to illustrate on the calculator how (1+1/A)^A goes towards e as A
becomes large so I wrote the following program.  Everything is fine until I
get to 10 x 10^13 because the value for B is greater than e.  I think this
is probably a rounding error but I don't know what is really happening.  I
understand what is happening when A is 10x10^14 --- at least I am assuming
that the overflow in the calculator allows 1/A to be undefined so from that
point on the calculator thinks it is rasing 1 to a power and thus yeilds 1.
I added the lines in the program to dispay the value of A and then played
around a bit.  When I increase A's value by multiples of 5 or 2, similar
things happened.  If I change the multiplier to 5 or 3, I eventually get
numbers on either side of e.  Also, if I change my seed, A, to 9, I get
weird results.  Can anyone explain what is happening here?  At the very
least, I have another example of how the calculator can 'lie'.

10 stor A
Lbl  1
(1+1/A)^A sto B
DISP  B
DISP  A
A*10 sto A
PAUSE
GOTO 1

Lisa Ledwith
Germantown Academy
Fort Washington, PA
Mathematics Teacher

lledw@ga.k12.pa.us


Follow-Ups: