Pop Quiz

You have ten minutes. Begin.

1

The infinite product is equal to 0, the infinite sum is equal to 1. Add the two together and you get 1.
I haven't seen 0.999...=1 bait in this form before.

>The infinite product is equal to 0, the infinite sum is equal to 1
wrong, they converge at 0 and 1.

I think the point is the product is the missing 0.0000000....01. if you agree the product is 0, then you have to agree the sum is 1

Yes, and their limit is equal to 0 and 1.

what operation did you perform to add limits? I must have missed the section defining those rules in calc. Here's your daily reminder that limits are functionals that take functions as their argument.

>10^∞
Brainlet

my mistake, should be 10^i

They don't need to be functions explicitly. They only need to be equivalent to some function.

In fact, functions are usually defined as series, not the other way around.

Clearly, there are two series so you can evaluate them at their limit to get the equivalent limit of the function defined by them.

The first part goes to 0 because [math]a_k=constant

... I don't even know what the first symbol is.

Protip: learn, or at least be familiar with the greek alphabet if you want to learn about math. That's the capital greek letter pi

>tfw Kurusu will never exist in this time line

0 + 9(10/9-1) = 1

>[math]n=\infty[/math]
When [math]n\not\in\mathbb{N}[/math] the sum is undefined
When [math]n\to\infty[/math] however, [math]x=1[/math]
Sums/products to infinity aren't defined without limits
Reminder: [math]\sum_{i=1}^\infty f(i)[/math] is just shorthand for [math]\lim_{n\to\infty} \sum_{i=1}^n f(i)[/math]

0

So it's defined, you just defined it

They take functions as argument, yes, I don't see how that's relevant. We're using lim(f+g)=lim(f)+lim(g) here.

Actually no, you confused me. The question is to compute lim f + lim g. So we compute both limits and add them together. We don't use linearity here we're just adding real numbers.

converge to*
if you wanna be anal about this do it right at least

no integration? no differentiation?

>10^n instead of 10^i
It's zero.

Product is zero

Sum = 9n/(10^n), which goes to zero. Individual linits exist therefore the limit of the sum is the sum of the limit so x=0

...

the x = 1 for all n.
i wonder what the limit could be