CAS bug: limit of (1+1/n)^n

[Steve Keeley]

If I ask for the limit as n->∞ of (1+1/n)^n in CAS (set to exact), I get the answer of 1.

If I do the same on my 50g I get the correct answer of e.

(I hope this post keeps me from getting purged again!)

[Angus]

I've just checked it: gives e to me on the prime. I entered the expression using the limes template. Just in case that could be of importance.
I have no idea nor explanation what could be the reason you get '1' (variable n defined, maybe? Could that do harm in any way?), but some wiser guys might find the error.

[Joe Horn]

(04-15-2014 03:50 AM)Steve Keeley Wrote:  If I ask for the limit as n->∞ of (1+1/n)^n in CAS (set to exact), I get the answer of 1.
If I do the same on my 50g I get the correct answer of e.

limit((1+1/n)^n,n,∞) returns e.
limit((1+1/n)^N,n,∞) returns 1.
Perhaps you accidentally typed "N" instead of "n"?

[Steve Keeley]

Thanks! I also used the limit template. But after you wrote that it worked for you I tried again and found what I did wrong. I entered:

lim (1+1/n)^n

rather than:

lim ((1+1/n)^n)

The second one gave the right answer.

I didn't have this problem on the 50g since I was in RPN mode. I entered:

2: '(1+1/n)^n'
1: 'n=+∞'

then hit the "limit" softkey.

[jebem]

At least on the Prime simulator it gives "e" as an answer as well.

[Tugdual]

(04-15-2014 08:41 AM)Steve Keeley Wrote:  Thanks! I also used the limit template. But after you wrote that it worked for you I tried again and found what I did wrong. I entered:

lim (1+1/n)^n

rather than:

lim ((1+1/n)^n)

The second one gave the right answer.

I didn't have this problem on the 50g since I was in RPN mode. I entered:

2: '(1+1/n)^n'
1: 'n=+∞'

then hit the "limit" softkey.

Well, I don't see the value of adding one more level of parentheses. To me this is clearly a bug.

[Han]

The extra parentheses are needed to prevent ambiguity between:

\[ \lim_{n\to \infty} (1+1/n)^n = \left( \lim_{n\to \infty} (1+1/n) \right)^n = 1^n = 1 \]

and

\[ \lim_{n\to \infty} (1+1/n)^n = \lim_{n\to \infty} \left( (1+1/n)^n \right) = e \]

Should the limit operator have precedence over exponentiation? or the other way around? To remove any doubt what you intended to compute, use the extra parentheses. (More reason for the devs to get RPN into a better state :-)