ratios of e

[dchawes2]

I think the following equation is true for all integers n:

-(eⁿ/e^n-1)= e

However, I can't figure out why (assuming it is true).

 

[Deleted member 4993]

I think the following equation is true for all integers n:

-(eⁿ/e^n-1)= e

However, I can't figure out why (assuming it is true).

It is NOT true.

 

[HallsofIvy]

For any non-zero number, not just "e", \(\displaystyle \frac{a^{n+1}}{a^n}= a^{(n+1)- n}= a^1= a\). Your formula is wrong because of that "-" in front.

 

[dchawes2]

Thank you!

 

[Steven G]

e is a positive number. No matter what power you raise it to, (pos, neg or 0) you get back a positive number. Now when you divide two such expressions you get a positive over a positive which is a positive. Now if you put a negative sign in front of a positive number it becomes a negative number. So -(eⁿ/e^n-1) is a negative number so it can't equal e which is a positive number.