is there methodology or branch of mathematics that allows to answers questions like this (as t trends towards infinite.)
>>16846607So close, Dawg.
>>16846607what's the question?
>>16846607obviously 0
>>16846607[math]\pi / 2[/math]
>>16846607Here's your answer.>>16846845
>>16846845>>16846929>>16846994>>16847001Treat it rigorously.
'nalhsis
>>16846607Biggest nerdslop thread on the board rn
>>16847816>Treat it rigorously.https://www.wolframalpha.com/input?i=Limit%5BSum%5BSin%5BE%5En%5D%2C+%7Bn%2C+0%2C+x%7D%5D%2F%28x+%2B+1%29%2C+x+-%3E+Infinity%5D
>>16847816>Treat it rigorously.The limit is 0. To evaluate lim (x∞) [1/(x+1)] ∑_{n=0}^{x} sin(e^n), observe that the terms sin(e^n) oscillate between -1 and 1. The sequence e^n mod 2π is equidistributed in [0, 2π) [...]. Thus, the average of sin(e^n) converges to (1/(2π)) ∫_0^{2π} sin(θ) dθ = 0. By the equidistribution theorem, the partial sum is o(x), so the ratio tends to 0. Numerical evidence supports this: for N=300, the average is approximately 0.049, decreasing like O(1/√N).
>>16848128>>16848138You missed showing that the summation is defined for non integer x
>>16848192>You missed showing that the summation is defined for non integer xI don't have a degree in ergodic theory.Try:1. George D. Birkhoff (1884 – 1944)2. John von Neumann (1903 – 1957)3. Andrey Kolmogorov (1903 – 1987)4. Hillel Furstenberg (1935 – )5. Yakov G. Sinai (1935 – )
>>16846607Fubini can be used here, right?
>>16848518Niels Fünkstorung (1967 - )
>>16851945>I'm a humanHe doesn't want to be one of them.He's glad that he's not one of them.The last thing he wants to be is one of them.
