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Math Help - simplification help

  1. #1
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    simplification help

    What are some ways of simplifying this and why:

    (k+1)^k^+^1

    Would this be one of them?

     (k+1)(k+1)^k
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  2. #2
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    Quote Originally Posted by webhound2 View Post
    What are some ways of simplifying this and why:

    (k+1)^k^+^1

    Would this be one of them?

     (k+1)(k+1)^k
    I like the first form.
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  3. #3
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    you could do something like this.

    <br />
\begin{aligned}<br />
(k+1)^{k+1}&=(k+1)(k+1)^{k} \\<br />
                &=k\cdot (k+1)^{k}+(k+1)^{k} \\<br />
\end{aligned}<br /> <br />
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by webhound2 View Post
    What are some ways of simplifying this and why:

    (k+1)^k^+^1

    Would this be one of them?

     (k+1)(k+1)^k
    If you wanted to expand it out you could use the binomial theorem

    \displaystyle (k+1)^{k+1}=\sum_{n=0}^{k+1}\binom{k+1}{n}k^n
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