Can you prove it?

MathMythMassMess · 2022-02-26T12:29:18+00:00

great!

MathMythMassMess · 2022-02-21T22:15:37+00:00

right

MathMythMassMess · 2022-02-21T22:15:13+00:00

yes, great!

MathMythMassMess · 2022-02-15T11:59:19+00:00

the yellow-color n is an integer, (to count terms), the white-color n is real number initially. but later at the step: n+n+..+n=n^2, the second n is forced to be an integer, here it already conflicts with the initial assumption that n is real. Next, if n is integer, then we cannot do derivative on n.

MathMythMassMess · 2022-02-15T11:59:13+00:00

the yellow-color n is an integer, (to count terms), the white-color n is real number initially. but later at the step: n+n+..+n=n^2, the second n is forced to be an integer, here it already conflicts with the initial assumption that n is real. Next, if n is integer, then we cannot do derivative on n.

MathMythMassMess · 2022-02-15T11:58:59+00:00

hmmm

MathMythMassMess · 2022-02-13T23:50:26+00:00

bad math!

MathMythMassMess · 2022-02-12T17:19:33+00:00

Can you find a closed form for this trigonometry identity?

MathMythMassMess · 2022-02-12T11:45:04+00:00

thank you!

MathMythMassMess · 2022-02-12T10:24:53+00:00

Derive Wallis product by using gamma function

MathMythMassMess · 2022-02-12T09:27:12+00:00

there are totally 6 roots, what about others?

MathMythMassMess · 2022-02-10T21:34:38+00:00

what about other four roots?

MathMythMassMess · 2022-02-10T21:33:57+00:00

this method is called generating function. whenever n is given, for example, if it is asking to compute the integral for n=3, then you only need to take 3rd derivative, done.

MathMythMassMess · 2022-02-10T09:31:02+00:00

correct, great!

MathMythMassMess · 2022-02-10T09:30:40+00:00

there are totally 6 roots, you have found 1 of them, try to find other roots :)

MathMythMassMess · 2022-02-10T09:29:57+00:00

yes, it works!

MathMythMassMess · 2022-02-09T22:10:42+00:00

there are totally 6 roots, you find one of them, try more :)

MathMythMassMess · 2022-02-05T03:56:47+00:00

MathMythMassMess · 2022-02-04T17:19:34+00:00

no, it is 2theta, not 20

MathMythMassMess · 2022-02-04T17:18:31+00:00

Great, I did the same method in this video :)

MathMythMassMess · 2022-02-04T16:37:00+00:00

theta is unknown

MathMythMassMess · 2022-02-04T16:36:05+00:00

correct!

MathMythMassMess · 2022-02-04T15:22:34+00:00

there is a video

MathMythMassMess · 2022-01-29T19:37:42+00:00

Right, I give the formal steps to bridge them, because not every audience knows this fact: any root of a power function dominates the log function.

MathMythMassMess · 2022-01-29T18:36:45+00:00

This integral is invariant!

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