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Anonymous at Mon, 10 Feb 2025 05:22:27 UTC No. 16580989
What are some ways to solve this?
Anonymous at Mon, 10 Feb 2025 07:20:19 UTC No. 16581037
>>16580989
Show it as a recursive sequence
Verify the monotonicity and the boundedness of the sequence
Use the formula a = f(a) to get its fix point
Anonymous at Mon, 10 Feb 2025 08:02:04 UTC No. 16581082
>>16580989
Set y=2+bullshit
Add 1 to both sides of x=1+1/bullshit such that x+1=2+bullshit=y
substitute in y so x+1=2+1/y=y
multiply both sides of 2+1/y=y by y to get 2y+1=y^2
subtract 2y-1 from both sides so 2=y^2-2y+1
rewrite it as 2=(y-1)^2
take the square root so sqrt(2)=y-1
add 1 so sqrt(2)+1=y
substitute back y=x+1 so sqrt(2)+1=x+1
subtract 1 from both sides so x=sqrt(2)
Or save yourself a bunch of time and just look up the rule because anything that regular is definitely a rule.
Anonymous at Mon, 10 Feb 2025 08:20:43 UTC No. 16581093
>>16580989
Start typing it into the calculator. Observe the result with the extra terms added.
> It seems to converge to 1.4142...
The result is sqrt(2)
Anonymous at Mon, 10 Feb 2025 08:29:25 UTC No. 16581097
>>16580989
[eqn]
x + 1
= 2 + \cfrac{1}{2 + \cfrac{1}{2 + \cfrac{1}{\ddots}}}
= 2 + \frac{1}{x + 1}
\\
(x + 1)^2 = 2(x + 1) + 1 \Longrightarrow x^2 - 2 = 0
\\
x = \pm \sqrt 2
[/eqn]
Jesus christ, Hiroshimoot. 15 minutes and three captchas just to post this.
Anonymous at Mon, 10 Feb 2025 08:47:45 UTC No. 16581105
>>16580989
x = Sqrt[2]
proof:
https://www.wolframalpha.com/input?
Anonymous at Mon, 10 Feb 2025 08:52:18 UTC No. 16581110
>>16580989
https://en.wikipedia.org/wiki/Simpl
Anonymous at Mon, 10 Feb 2025 09:00:12 UTC No. 16581119
>>16581093
>the calculator
the or a?
Sherlock Holmes at Mon, 10 Feb 2025 09:10:13 UTC No. 16581121
>>16581110
>https://en.wikipedia.org/wiki/Simp
Oh, so you're using a stationary device, like a desktop, ay?
You should have replaced "en.wikipedia" with "en.m.wikipedia" in your URL.
Then we would have concluded, that you're using a mobile device, like a tablet.
good grief at Mon, 10 Feb 2025 09:20:01 UTC No. 16581124
>>16581097
omg he wrote: x^2 – 2 = 0
instead of: x^2 = 2
and then he wrote: x = +–Sqrt[2]
even though: x > 0
Anonymous at Mon, 10 Feb 2025 09:48:36 UTC No. 16581132
>>16581119
The if it isnt a complex number
Anonymous at Mon, 10 Feb 2025 13:01:07 UTC No. 16581238
>>16581230
>e – 1
"In a 1945 Popular Astronomy magazine article, the science writer D.E. Richardson apparently independently arrived at the same conclusion as Blagg: That the progression ratio is 1.728 rather than 2."