Final answer:
A proof that a given recursive sequence t(n) is O(n²), which involves demonstrating that the sequence grows at a rate no faster than n squared, according to the Big O notation in mathematics.
Step-by-step explanation:
The recursive relation t(n) = t(n-1) × n is O(n²), which pertains to the complexity analysis in mathematics, specifically within the context of algorithm analysis or sequences. In this context, the Big O notation describes the upper bound of the complexity, meaning it provides a way to describe the worst-case scenario of how the runtime of an algorithm grows with respect to the size of the input.
To show that t(n) is O(n²), we can use mathematical induction or other direct methods like summing up a series. For example, for t(n) being the sum of the first n terms of an arithmetic progression, proofs would typically involve manipulating series expressions and possibly utilizing results from calculus or discrete mathematics, such as the binomial theorem.