- #1
Paul_G
- 3
- 0
Hi!
I'm currently taking a fairly early stats course, and I'm having a bit of a hangup learning exactly how to use "moments" properly. My general solution whenever I run into problems internalizing things is to do a bunch of easy problems, and to show it from the ground up.
This is my first post here, so I'm not certain how to use the math notationy stuff.
My issue here is fairly simple - I want to show that e = lim n-> inf (1+1/n)^n = 1/0!+1/1!+1/2!+...
So I start with my n-> inf (1+1/n)^n and do binomial expansion.
So e = lim n-> Infinity Sum[(n choose k)*1/n^k, {k, 0, Infinity}].
From here, we can go to Sum[n!/(n-k)!k! * 1/n^k, {k,0,Infinity}]
Next... Okay, next we can change the numerator to (n-1)! and the denominator of the right to n^(k-1), but I have no idea what I can do next, considering I'm trying to get to Sum[1/k!,{k,0,Infinity}]. How do I remove the n's?
Thank you very much, and apologies for the mess.
I'm currently taking a fairly early stats course, and I'm having a bit of a hangup learning exactly how to use "moments" properly. My general solution whenever I run into problems internalizing things is to do a bunch of easy problems, and to show it from the ground up.
This is my first post here, so I'm not certain how to use the math notationy stuff.
My issue here is fairly simple - I want to show that e = lim n-> inf (1+1/n)^n = 1/0!+1/1!+1/2!+...
So I start with my n-> inf (1+1/n)^n and do binomial expansion.
So e = lim n-> Infinity Sum[(n choose k)*1/n^k, {k, 0, Infinity}].
From here, we can go to Sum[n!/(n-k)!k! * 1/n^k, {k,0,Infinity}]
Next... Okay, next we can change the numerator to (n-1)! and the denominator of the right to n^(k-1), but I have no idea what I can do next, considering I'm trying to get to Sum[1/k!,{k,0,Infinity}]. How do I remove the n's?
Thank you very much, and apologies for the mess.