# Thread: Limit of a Sum

1. ## Limit of a Sum

How would one work out this limit?

lim 48(sum(x^n/n! -x -1))/x^2
x->0

im sorry for the formatting... thanks in advance

2. Originally Posted by CalcGeek31
How would one work out this limit?

lim 48(sum(x^n/n! -x -1))/x^2
x->0

im sorry for the formatting... thanks in advance
If you mean $\lim_{x \to 0} \frac{48}{x^2} \left( \sum_{n=0}^{\infty} \frac{x^n}{n!} - 1 - x\right)$

it's $\lim_{x \to 0} \frac{48}{x^2} \left(1 +x + \frac{x^2}{2!} + \frac{x^3}{3!} \cdots - 1 - x\right) = \lim_{x \to 0} \frac{48}{x^2} \left(\frac{x^2}{2!} + \frac{x^3}{3!} \cdots \right)$ = $\lim_{x \to 0} 48 \left(\frac{1}{2!} + \frac{x}{3!} \cdots \right) =24$

3. everything is over x^2

4. Originally Posted by CalcGeek31
everything is over x^2
In that case you've been shown the solution.