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Xforce Keygen [CRACKED] ReCap Pro 2018 32 Bit Windows 10

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Q:

Summation on an equation involving exp(2i$\pi$n)

For n=3,4,5,6,7,8,9,10,11,12,13,14,15,16,17…
Lets suppose that i define the function
$f(n) = \sum_{n=3}^{n=\infty} e^{i\pi n}$
Which means
$\sum_{n=3}^{n=\infty} e^{i\pi n} = \sum_{n=3}^{n=\infty} 1$
Now i’m trying to find the sum for L=1,2,3,4,5,6,7,8,9…
i am finding the sum to be
$(1-1)+(1-1)+(1-1)+…….$
My question here is:

How do i use this to find for L=1,2,3,4,5,6,7,8,9…
what about the general form of this sum? Is there any general form for this type of sum?

Example:
The sum of L=3,4,5..,12 is
$f(3) + f(4) + f(5) + \dots + f(12)$

A:

Yes, you have it right and the general formula is $$\sum_{k=1}^n\textrm{e}^{i\pi n}=\textrm{e}^{i\pi n}\sum_{k=1}^n\textrm{e}^{i\pi}=\textrm{e}^{i\pi}\left(1+\textrm{e}^{i\pi}+\textrm{e}^{2i\pi}+\dots+\textrm{e}^{ni\pi}+\dots+\textrm{e}^{(n-1)i\pi}\right)$$

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