Why the "limit" is bullshit

If you don't make the effort to format your post correctly with latex, then I wont make the effort to respond to it seriously

Why does this need latex? just read

>>8931611
The series converges at 0 because the function 1/n+1/n... where n goes to infinity represents a series of infinitesimally small quotients.

I know this is not a rigorous explanation but that's how I was taught to understand it

>>8931648
No. Do it right.

>>8931611
I don't understand your question at all.

>>8931666
how can you dont understand it?

>>8931611
>tell me why

you selectively choose some of the n's in the expression to take the limit at infinity for, then do some bullshit operations, then take the limit again for the same variable, this time taking it for the other n's in the expression

not sure why you think this is okay

>>8931611
>n/n =1/n+1/n+1/n+1/n+...

?

>>8931676
what's wrong??

>>8931680
>>8931611

[math]\frac{n}{n}[/math] for "n" going to infinity, the expression is in indeterminate form. So there's some errors in your notation. However, I understand what you're trying to ask
>>8931653
This explanation is the best so far, I suggest you read up on the properties of convergent series, then it'll be somewhat obvious why the answer is zero. Proving this is another story, but it's kinda unnecessary.

>>8931721
then

lim n->inf, 1/n=0

n/n=(1/n)*n

what is it?

>>8931729
Zero times infinity equals ???

>>8931738
what?

>>8931742
The limit of one over n as n approaches infinity equals one over infinity which equals zero.

The limit of n as n approaches infinity is infinity.

Consequently, the limit of one over n as n approaches infinity times the limit of n as n approaches infinity equals zero times infinity, which is undefined.

In other words, zero times infinity equals ???

>>8931729
1, by L'hopital's rule

>>8931757
https://www.wolframalpha.com/input/?i=lim+n-%3Einf+0*n

>>8931611
>1/n+1/n+1/n+1/n+...
what does this mean OP?

>>8931951
(1/n)*n

LaTex or die niggas

[math] \displaystyle{\lim_{n \rightarrow \infinity} \frac{1}{10^n} = 0} [/math]

seems right graphically

>>8931611
>tell me why
Why what?
You are taking the limit of n*(1/n) and are arguing that it goes to 0.

This batshit insane and if you have the slightest knowledge about calculus you should understand that just because 1 term in a series goes to 0 the whole series doesn't need to go to 0.

>>8931611
>n/n=0
No.
Lrn2arithmetic

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11KB, 480x360px

>>8931611

>>8931611
In general [math]\lim_{n\to\infty} a_n + b_n = \lim_{n\to\infty}a_n + \lim_{n\to\infty}b_n[/math] holds for a fixed finite number (here two) of summands (if the limits exist).