I Have a small problem.(adsbygoogle = window.adsbygoogle || []).push({});

I know the following:

The series:

[tex]

S_{n} = 1 + 2 + 3 + 4 + 5 = \sum_{i=1}^{n=5}i

[/tex]

[tex]

2S_{n} = 1 + 2 + 3 + 4 + 5 + 1 + 2 + 3 + 4 + 5 = n(n+1) = n^{2} + n

[/tex]

Therefor:

[tex]

S_{n} = \frac{2S_{n}}{2} = \frac{n^{2} + n}{2}

[/tex]

[tex]

\sum_{i=1}^{n=5}i = \frac{n^{2} + n}{2} = \frac{25 + 5}{2} = 15

[/tex]

Ok, thats simple.

But i was attempting to do the same with the factorials, where:

[tex]

ln(n!) = ln(5!) = ln(1) + ln(2) + ... + ln(5) = \sum_{i=1}^{n=5}log(i)

[/tex]

Is it possible to apply the same method, or something similar here? I did try a few but got a bit cheesed off.

In the first case, you just duplicate and reverse the sequence and add to get a constant sequence.

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# Factorials & Series - im a little lost here

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