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Can someone draw a plot for this function?

$ f(x) = \begin{cases} \sum_{i=2}^{x}\left(\frac{\prod_{k=1}^{i-1}\left(2k-1\right)\,\cdot\,-\left(-\frac{1}{2}\right)^{i}}{i!}\right) + \frac{3}{2} & x \geq 2 \\ \\ \frac{3}{2} & x = 1 \\ \\ 1 & x=0 \end{cases} \,\,\,\,\, \land \,\,\, x \in \mathbb{N} $

I came up with this formula in class, and if I'm correct, the $\lim_{x\to+\infty}f(x) = \sqrt{2}$.

Thanks in advance!

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  • $\begingroup$ Wolfram|Alpha surely can. $\endgroup$ – Ruslan Apr 25 '16 at 16:47
  • $\begingroup$ That might be true, though I have no idea how to tell WolframAlpha to plot that... there are too many variables in it. $\endgroup$ – Riccardo Bello Apr 25 '16 at 16:55
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http://puu.sh/ovoEI/659af782b3.png - Can't post images as my $reputation < 10$.

I could finally plot the function myself with Geogebra and CAS. It looks like I'm right, and that as $x\to+\infty$ the function (the red line) gets closer and closer to $\sqrt{2}$, represented by the green line.

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