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how to sovle array which odd and even have difference recursive function


RSolve[{(b[n] == 1 + b[n/2] && Mod[n, 2] == 0) && (b[n] == 1/n &&
Mod[n, 2] == 1)}, b[n]==2, n]   failed to work !
        when n  is odd   b[n] == 1/n
        when n  is even  b[n] == 1 + b[n/2]



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