I have two summation formulae \begin{align*} s(n)=\sum_{p=0}^{n}\binom{n}{p}\frac{(\sqrt{2})^p k^{n-p}}{\mathrm{i}^{p}} \end{align*} and \begin{align*} s(n+2)=\sum_{p=0}^{n+2}\binom{n+2}{p}\frac{(\sqrt{2})^p k^{n+2-p}}{\mathrm{i}^{p}} \end{align*} where $\mathrm{i}$ is unit imaginary number. How can we write $s(n+2)$ in terms of $ s(n)$?
Relation between two summation
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summation
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0Is there anything special about the i that looks different? – 2017-01-30
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1Welcome to [MSE](http://math.stackexchange.com). It is mandatory on this site to add your own attempts and where you face problems, then others can help you. – 2017-01-30
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0$s(n+2)=s(n)+\text{thing inside the sum}(n+2)+\text{thing inside the sum}(n+1)$ – 2017-01-30
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0Thats right.....I am looking for something multiple? – 2017-01-30