What is closed form of $1!+2!+3!+\cdot\cdot\cdot n!$
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
141390
Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
63553
Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$
35855
Closed form for an infinite product
58972
Proof/Derivation of Closed form of Binomial Expression $\sum\limits_{k=0}^{2n}(-1)^k\binom{2n}{k}^2$
45862
Nested sum of binomial coefficient in closed form
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
133420
Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
34767
Proving $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)<3$ for all positive integers $n$
70611
Prove by Mathematical Induction: $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$
42736
Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
119606
Closed form of summation
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
25426
A sum of series problem: $\frac{3}{1!+2!+3!} + \frac{4}{2!+3!+4!} + \cdots + \frac{2008}{2006!+2007!+2008!}$