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Math Help - help me to simplify this factorial

  1. #1
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    help me to simplify this factorial

    from (k+1)! -1 + (k+1)(k+1)! to (k+2)! - 1
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  2. #2
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    \begin{array}{l}<br />
 \left( {k + 1} \right)! - 1 + \left( {k + 1} \right)\left( {k + 1} \right)! \\ <br />
 \left( {k + 1} \right)!\left[ {1 + \left( {k + 1} \right)} \right] - 1 \\ <br />
 \left( {k + 2} \right)! - 1 \\ <br />
 \end{array}<br /> <br />
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  3. #3
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    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

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