#Program to verify recurrence (43) Theta =  1 in Clote, Kranakis, Krizanc

# D. Krizanc

def U(n):

    u2=0.
    u3=1.
    u4=1.
    for i in range(5,n+1):

        x = 1./(i-2.) +  u4*(i-3.)/(i-2.) + (u3+u2)/(i-2.)
        u2 = u3
        u3 = u4
        u4 = x
        if i%10000==0:
            print i, x, x/i

    return x
        
U(1000000)