What is the sum of this power series?

Question

This is the series: $$ \sum_{n=1}^\infty \frac{x^{2n}}{(2+\sqrt{2})^n} $$

My problem is that I don't know how to rid of that $ (2+\sqrt{2})^{-n} $.

user17762 · Accepted Answer · 2013-01-21 18:20:35Z

up vote 4 down vote accepted

HINT Let $y = \dfrac{x^2}{2+\sqrt{2}}$ and see what happens.

answered Jan 21 at 18:20

user17762
76.1k8106230

Is it really that easy?:)) – dragostis Jan 21 at 18:27

Jonas Meyer · Answer 2 · 2013-01-21 18:21:05Z

up vote 1 down vote

I recommend using the identities $x^{2n}=(x^2)^n$ and $\dfrac{a^n}{b^n}=\left(\dfrac{a}{b}\right)^n$.

answered edited Jan 21 at 18:21

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