The lies about photos from space and space flight don't count.

Rewriting cuz i fucked up
Can I prove that $\sum_{k=1}^{\infty}\frac{1}{k}$ diverges by showing it's a geometric series? Idk if anyone has done this yet but I'd like to know because I think I've found a way to do it, but I'm not a big mathhead so I don't know if someone already prove it's impossible or not.

Holy shit this movie was so annoying.

What scientific facts are illegal to publish in your country?

vaxxxies are responsible for this

Give me a reason why I shouldnt breed with my sister

feel free to solve the problem too to get some context but I was intrigued by a part of it

This is the problem
>A faucet A takes 2 hours more than a faucet B to fill the same container. First they're opened at the same time for 1.5 hours. After that, faucet B is closed and then faucet A finishes filling the container in 1 hour. How long would each faucet take to fill the tank separately?
Solving this problem (leads to what I want to ask, spaced to let you try it first)

Since A = B + 2 I will call B as x to simplify things

In A hours faucet A fills 100%, so in 1 hour it fills 1/(x + 2)
In B hours faucet B fills 100%, so in 1 hour it fills 1/x

In 1 hour, faucets A and B fill 1/x + 1/(x+2)

In 1.5 hours both faucets fill 3(x+1)/(x(x+2))

In 2.5 hours the entire thing is filled, which gives the equation 3(x+1)/(x(x+2)) + 1/(x + 2) = 100%

Which leads to this equation x^2 - 2x + 3 = 0

My question is

What does the solution x = -1 mean? It solves the quadratic equation but if you substitute it in the other equations it gives nonsensical results (like in 2.5 hours 0 of the container is filled, while in 1 hour the container is filled and emptied simultaneously?). Why does -1 solve the equation but gives the result that faucet A fills the entire thing in 1 hour and faucet B empties the entire container in 1 hour?

Can a photon have so little energy that it can't leave Earth's gravity and will fall back down?

Can I prove that $\frac{1}{k}$ converges by showing it's a geometric series? Idk if anyone has done this yet but I'd like to know because I think I've found a way to do it, but I'm not a big mathhead so I don't know if someone already prove it's impossible or not. Pic unrelated

Just found out I might have CO poisoning, school has been rough the last few months and I just thought I was retarded