# Thread: help me to simplify this factorial

1. ## help me to simplify this factorial

from (k+1)! -1 + (k+1)(k+1)! to (k+2)! - 1

2. $\begin{array}{l}
\left( {k + 1} \right)! - 1 + \left( {k + 1} \right)\left( {k + 1} \right)! \\
\left( {k + 1} \right)!\left[ {1 + \left( {k + 1} \right)} \right] - 1 \\
\left( {k + 2} \right)! - 1 \\
\end{array}

$

3. Hello, TheRekz!

Simplify: . $(k+1)! -1 + (k+1)(k+1)!\quad\Rightarrow\quad (k+2)! - 1$

We have: . $(k+1)! - 1 + (k+1)(k+1)! \;=\;(k+1)(k+1)! + (k+1)! - 1$

Factor out $(k+1)!$ from the first two terms: . $(k+1)!\cdot[(k+1) + 1] - 1$

. . And we have: . $\underbrace{(k+1)!(k+2)}_{\text{This is }(k+2)!} - 1$

Therefore, we get: . $(k+2)! - 1$