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I'd love to help you, but series is not my speciality, so I don't know much about it. Still, what I do know, is that the expected value of that series (which is not calculus, but probablity) IS 1/2, but that's not the result of the series, it's like an average of a thousand of experiments, just as if you rolled a dice infinite times, the expected value (that is, the average of all the result) would be 3.5, even though you'd never get that result in the dice.

Also, you spelled matemáticas wrong, the accent goes on the second a, not the third And you forgot an s, "las matemáticas)