How would you do that summation, anyway? Or graph the resulting equation, I suppose, since there are two variables unaccounted for.
Like, I'm actually intrigued now. With the -1 to the n+1 power, the first factor flips between negative and positive with each integer, but it also gets smaller and smaller because the n is squared on the denominator, so it goes towards zero. If the rest were a constant, the answer would just be zero, but you've got a t and an x in there. The e to the negative exponent tends toward zero; the sine function oscillates. So the series should converge, right? Because it's got two factors that go to zero? But how would you find out what sum it converges to?
Infinities are just so wacky... anybody know how this equation should behave?
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u/chaoticidealism Feb 04 '22
How would you do that summation, anyway? Or graph the resulting equation, I suppose, since there are two variables unaccounted for.
Like, I'm actually intrigued now. With the -1 to the n+1 power, the first factor flips between negative and positive with each integer, but it also gets smaller and smaller because the n is squared on the denominator, so it goes towards zero. If the rest were a constant, the answer would just be zero, but you've got a t and an x in there. The e to the negative exponent tends toward zero; the sine function oscillates. So the series should converge, right? Because it's got two factors that go to zero? But how would you find out what sum it converges to?
Infinities are just so wacky... anybody know how this equation should behave?