$1!+2!+3!...$ The sum of all the factorials up to a chosen positive integer $n$. This would be expressed using sigma notation. If you can show me this, that would be enough for me, for now.

If you can, show this for $(n-1)$, for the formula which I am making says, to find the $5^{th}$ harmonic number, add all the factorials from $1!$ up to $4!$, that is, the sum of all positive integer factorials from $1!$ to $(n-1)!$.

If you know how to set this up, it is gamma of two plus gamma of three plus gamma of four plus gamma of five, using the example of the $5^{th}$ harmonic number. Simply, it is $1+2+6+24$ that I am seeking to express. It is a small part of the formula.

  • $\begingroup$ Please use MathJax and clarify your post. I don't really understand what's the question. $\endgroup$ – rubik Aug 22 '16 at 5:42

It sounds like you want $$\large\sum_{k=1}^{n} k!$$ which represents the sum $1!+2!+\cdots+n!$ using sigma notation. The choice of letter $k$ is irrelevant, you are free to choose any other symbol (besides $n$, which is already being used).

In LaTeX, this is written \sum_{k=1}^{n} k!.

  • $\begingroup$ That is basically what I need for now. $\endgroup$ – Jeffrey Young Aug 22 '16 at 6:05

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