Infinite sums and products 5 (#20)

Calculus Level pending

Find the value of S.

\[ 1+\frac{1}{1*3} + \frac{1}{1*3*5} + \frac{1}{1*3*5*7} + \ldots = S(1-\frac{1}{2*1!*3}+\frac{1}{2^2 * 2!*5} -\frac{1}{2^3 *3!*7} + \ldots) \]

Note 1: Round to two decimals
Note 2: I would like to have a personal private meeting in online to share this kind of infinite series problems. I have 680 problems of infinite series, products and recurrence sequences and would like to have solutions for each problems which I do not have.


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