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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).

See The Solution Submitted by Larry    
Rating: 4.5000 (2 votes)

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  Subject Author Date
Some ThoughtsSolutionbroll2020-11-01 00:21:07
keto dietSamantha Allan2020-10-30 16:06:34
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