Let the increasing sequence of integers D: d₁, d₂, d₃, ...d_n-1, d_n... represent the sequence of consecutive differences of another sequence T: t₁, t₂, t₃, ...t_n-1, t_n.

Given t₁=0 , and t_k-t_k-1=d_k-1=k, provide definition and formula for the sequence T.