What i have so far:

Xn~N(1,1/n)

b1>0 b2>0 , ... , bi>0

P(X=1)=b1 , ... , P(X=i)=bi

so Xn has c.d.f

b1ϕ(x) + ... + biϕ(x)

(the mean of each phi above increases by 1 and starts at 1)

(theres also a subscript after the phi on the bottom that increases by 1 and starts at 1)

Does this make sense?