3 ms·
How do you define infinite power? A limit of such series, if exists? {x, x^x, x^x^x, ...}
by H8crilA 7y ago
How do you define infinite power? A limit of such series, if exists?
{x, x^x, x^x^x, ...}
- lokedhs 7y agoThat would be equal to x^y, which means that the solution is the y'th root of y? However, don't you have to prove that the series converges? Is the approach even valid if it doesn't?
- deleted 7y ago[deleted]
- jwilk 7y agoNote that according to your solution, x=√2 for both y=2 and y=4. But of course the sequence cannot converge to both 2 and 4 at the same time!
- a1369209993 7y agoFixed point of x^(...), I guess; you don't actually need to define it properly: x^x^x^... = y x^(x^x^x^...) = x^(y) x = y^(1/y) # there you go