perplexus.info :: Sequences : Name the sequence

Name the sequence (Posted on 2018-09-17)

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.

No Solution Yet Submitted by Ady TZIDON

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soln

| Comment 1 of 5

I assume T is also infinite (..., tn, ...)

with d_k-1 = k

D: 2, 3, 4, 5,...

so, adding

T: 0, 2, 5, 9, 14...

so tn = sum[{i=2:n} i ] = sum[ {i=1:n} i ] -1 = n(n+1)/2 -1

Posted by Steven Lord on 2018-09-17 08:58:52

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