因为概率和是1
P(E=n)=a/n(n+1)=a[1/n-1/(n+1)]
所以P(E=1)+P(E=2)+P(E=3)+P(E=4)
=a[(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)]
=a(1-1/5)
=4a/5=1
所以a=5/4
故数学期望是E=1*P(E=1)+2*P(E=2)+3*P(E=3)+4*P(E=4)
=(5/4)*[(1/1-1/2)+2(1/2-1/3)+3(1/3-1/4)+4(1/4-1/5)]
=(5/4)*(1/2+1/3+1/4+1/5)
=77/48