- #1
krackers
- 72
- 0
Limit proof that 1=0 -- Where is the error?
[itex]\lim_{n\to\infty } 1=\lim_{n\to\infty }\frac{n}{n}=\lim_{n\to\infty }\frac{\overbrace{1+1+\ldots+1}^{n \text{ times}}}{n}=\lim_{n\to\infty }\frac{1}{n} + \lim_{n\to\infty }\frac{1}{n} + \ldots=0[/itex]
I have a feeling it is in the step where you split the limit of a sum into the sum of the limit of the terms, but I do not have any exact explanation as to why. Can anyone help?
[itex]\lim_{n\to\infty } 1=\lim_{n\to\infty }\frac{n}{n}=\lim_{n\to\infty }\frac{\overbrace{1+1+\ldots+1}^{n \text{ times}}}{n}=\lim_{n\to\infty }\frac{1}{n} + \lim_{n\to\infty }\frac{1}{n} + \ldots=0[/itex]
I have a feeling it is in the step where you split the limit of a sum into the sum of the limit of the terms, but I do not have any exact explanation as to why. Can anyone help?