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SumConvergence[( Product[(2 n - 1), {n, 1, infinity}])/n!, n]

$$\sum_1^\infty{\frac{1\times3\times5\times...\times(2n-1)}{n!}}$$

However this returns True but it isn't true.

So how can I test it ?

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    $\begingroup$ Your product is incorrect. Try Product[(2 k - 1), {k, 1, n}] $\endgroup$
    – ybeltukov
    Jan 22, 2015 at 11:22
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    $\begingroup$ Also, note that Product[(2 k - 1), {k, 1, n}] can be written more compactly using double factorial (Factorial2) notation, i.e., (2n-1)!! $\endgroup$
    – Bob Hanlon
    Jan 22, 2015 at 14:02
  • $\begingroup$ Infinity. Not infinity for one. $\endgroup$ Jan 22, 2015 at 14:27
  • $\begingroup$ Also, please use accepted mathematical notation by stating the iteration variable name: Sum_{n=1}^Infinity. Without this specification, the mathematical statement of your sum clearly diverges. Your title, too, should state "sum" rather than "product." $\endgroup$ Jan 22, 2015 at 17:59

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