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This problem came to my intentions when I was attempting to find the answer in https://www.physicsforums.com/showthread.php?t=263571".
The sum of the sequences of a series can be calculated if the series is:
a) Arithmetic Progression by ~ [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
b) Geometric progression by ~ [tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
My question is, are formulas or basic ideas needed to used to find the product of the series, rather than the sum.
e.g. [tex]1+2+3+...+(n-1)+n=\frac{n^2+n}{2}[/tex]
However, what about:
[tex](1)(2)(3)...(n-1)(n)=x[/tex] where x is the product in terms of n.
I am not looking for the answer, but would appreciate if anyone shows how to approach this problem; rather than the usual guesses I've been taking...
The sum of the sequences of a series can be calculated if the series is:
a) Arithmetic Progression by ~ [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
b) Geometric progression by ~ [tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
My question is, are formulas or basic ideas needed to used to find the product of the series, rather than the sum.
e.g. [tex]1+2+3+...+(n-1)+n=\frac{n^2+n}{2}[/tex]
However, what about:
[tex](1)(2)(3)...(n-1)(n)=x[/tex] where x is the product in terms of n.
I am not looking for the answer, but would appreciate if anyone shows how to approach this problem; rather than the usual guesses I've been taking...
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