Limits

[Luca Gvr]

I need help with the following limit

 

[Deleted member 4993]

I need help with the following limit

Use:

k! + (k+1)! = k! * (k+2)

simplify the denominator.

 

[AmandasMathHelp]

It might help to know why the above works.. basically you are factoring out a k! out of both terms.

[MATH]k! + (k+1)! = k! + (k+1)*k!= k!* (1+k+1)[/MATH]
You can apply that idea to the entire bottom of the fraction. Then you'll be able to simply stuff after that. The following limit may be helpful . It's likely you do not need to prove this fact because the proof is a bit difficult.

[MATH] \sum_{n=1}^{\infty} \frac{1}{n!} = e [/MATH]

 

[lookagain]

[MATH] \sum_{n=1}^{\infty} \frac{1}{n!} = e [/MATH]

That sum equals \(\displaystyle \ e - 1. \ \ \) You need to start with n = 0.

 

[AmandasMathHelp]

Ohhhh yep. My mistake