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Sums of Sums of Triangular Numbers (Posted on 2020-09-05) Difficulty: 2 of 5
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.

...

Tk(n) is the sum of the first n Tk-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 Tk(n)?

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

No Solution Yet Submitted by Larry    
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