Mathematically prove that a Beta prior distribution is conjugate to a Geometric likelihood function

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Shivam Dave

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Shivam Dave Asks: Mathematically prove that a Beta prior distribution is conjugate to a Geometric likelihood function
I have to prove with a simple example and a plot how prior beta distribution is conjugate to the geometric likelihood function. I know the basic definition as

'In Bayesian probability theory, a class of distribution of prior distribution $\theta$ is said to be the conjugate to a class of likelihood function $f(x|\theta)$ if the resulting posterior distribution is of the same class as of $f(\theta)$.'

But I don't know how to prove it mathematically.

P.S. - It would really nice of you guys to provide some good material on bayesian statistic and probability theory.

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After applying a scaling factor to my LANDSAT collection 2 level 2 data the values seem to be off.

screen capture of code and output

Code: 
var addNDVI = function(image) {
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Tanmoy Pati Asks: Parallel transport in curved spacetime
This is sort of a very introductory question and I am not finding any reference regarding this. And let me know whether my answer is correct or not.

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