Anyone knows in Calculus 2 why Geometric and Harmonic Series are called so?
Any ideas feel free!
Thanks!

Yes, the geometric series is recognized with their variables "a" and "r".
i.e. a+ar+ar^2+ar^3.....etc

as you may observe, "a" is the first term, while "r" is a constant # that is multiplied by each term in the sequence.
It is called geometric because it portrays a method mentioned above that is pattern-like.

The harmonic series I believe is called so because it is in form 1/n, where it is a classic divergence example. As a result, it is easier to expect what happen without further analysis,...."harmonic" for "expectancy to diverge".

Yes, the geometric series is recognized with their variables "a" and "r".
i.e. a+ar+ar^2+ar^3.....etc

as you may observe, "a" is the first term, while "r" is a constant # that is multiplied by each term in the sequence.
It is called geometric because it portrays a method mentioned above that is pattern-like.

The harmonic series I believe is called so because it is in form 1/n, where it is a classic divergence example. As a result, it is easier to expect what happen without further analysis,...."harmonic" for "expectancy to diverge".
I do know this but i need some kind of history probably why it was called so why geometric but not something else and so on.
Anyway Thanks!

You are probably asking about arithmetic, geometric, and harmonic sequences (aka progressions) rather than series-es. People commonly confuse the two.

Here look at this link: http://www.nexusjournal.com/GA3-4-Wassell.html

key terms to look for: arithmetic mean, geometric mean, harmonic mean.

For arithmetic progression if you plot all points on a plane you'll get a line. The growth of the sequence is linear. If you take n-th element, it will be an arithmetic mean of n-1 st and n+1 st elements. Hence it is called an arithmetic progression.

For geometric progression if you plot all points on a plane you'll get an curve of an exponential function. The growth of the sequence is exponential. If you take the n-th element, it will be a geometric mean of the n-1 st and n+1 st elements (i.e. the square root of their product). Hence it is called a geometric progression.

For harmonic progression the n-th term will be a harmonic mean of the n-1 st and n-2 nd elements (i.e. twice their product over their sum)

There is a difference between proportion in geometric progression and harmony in harmonic progression)

Here is another link to see the differences of all three means and all three progressions: http://www.aboutscotland.com/harmony/prop6.html