Problem 1. Find an expression for the triangular numbers Tn as follows. Explain why the nth triangular number Tn is given by Tn = 1 + 2 + 3 + 4 + ... + n. Compute a formula for 2Tn as follows: 2Tn = 1 + 2 + 3 + ... + (n - 2) + (n - 1) + n + Tn = n + (n - 1) + (n - 2) + ... + 3 + 2 + 1 2Tn = [fill in] Deduce formula for Tn.
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A triangular number is the sum of the first n natural numbers. So, the nth triangular number Tn can be represented as the sum of the first n natural numbers: Tn = 1 + 2 + 3 + ... + n Show more…
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