What are some ways of simplifying this and why: $\displaystyle (k+1)^k^+^1$ Would this be one of them? $\displaystyle (k+1)(k+1)^k$
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Originally Posted by webhound2 What are some ways of simplifying this and why: $\displaystyle (k+1)^k^+^1$ Would this be one of them? $\displaystyle (k+1)(k+1)^k$ I like the first form.
you could do something like this. $\displaystyle \begin{aligned} (k+1)^{k+1}&=(k+1)(k+1)^{k} \\ &=k\cdot (k+1)^{k}+(k+1)^{k} \\ \end{aligned} $
Originally Posted by webhound2 What are some ways of simplifying this and why: $\displaystyle (k+1)^k^+^1$ Would this be one of them? $\displaystyle (k+1)(k+1)^k$ If you wanted to expand it out you could use the binomial theorem $\displaystyle \displaystyle (k+1)^{k+1}=\sum_{n=0}^{k+1}\binom{k+1}{n}k^n$
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