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Compute a histogram of the time for a random walk, with the walker taking steps of ±1 to return to his/her starting position

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Compute a histogram of the time for a random walk, with the walker taking steps of ±1 to return to his/her starting position. If T is the return time show that P ( T = t/2)  ≈  /ζ(3/2),  where the normalisation constant ζ(3/2) ≈ 2.61 is the Riemann zeta function. Use this fact to show that a random walker will return to his/her starting position with probability arbitrarily close to 1, but the expected return time is infinite.