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n n! n-i i
t B (t)= t ──────── (1-t) t
i (n-i)!i!
i+1 (n+1)! (n+1)-(i+1) i+1
= ─── ──────────────────── (1-t) t
n+1 ((n+1)-(i+1))!(i+1)!
i+1 k! k-(i+1) i+1
= ─── ──────────────── (1-t) t , where k = n + 1
k (k-(i+1))!(i+1)!
i+1 k
= ─── B (t)
k i+1