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Sums of Sums of Triangular Numbers (Posted on 2020-09-05)

Let T₁(n) be the n-th Triangular number, the sum of 1 + 2 + ... + n.

T₂(n) is the sum of the first n Triangular numbers.

T₃(n) is the sum of the first n T₂(n) numbers.

...

T_k(n) is the sum of the first n T_k-1(n) numbers.

Please derive closed form expressions for each of T₁(n), T₂(n), and T₃(n). Describe the technique you used for the derivation.

Bonus: what is the formula for T_k(n)?

Bonus 2: prove the validity of your formula for T_k(n).

See The Solution Submitted by Larry

Rating: 4.5000 (2 votes)

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