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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Factorials & Series - im a little lost here

**Physics Forums | Science Articles, Homework Help, Discussion**