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Just a note

Proportion in older age groups  =  N0S + N0S2....+ N0S
N0 + N0S + N0S2....+ N0S
   =  S (N0 + N0S + N0S2....+ N0S)
    N0 + N0S + N0S2....+ N0S∞−1
   ≈   S