Grades 11-12 Video Solutions 2014-11&12 Video Solutions 2014 problem29

11&12 Video Solutions 2014 problem29

Video Transcription

Video Summary

The function \( f \) is recursively defined with \( f(4) = 6 \) and \( x \times f(x) = (x-3) \times f(x+1) \). Solving recursively, \( f(x) \) is expressed as a product involving three consecutive integers. This pattern reveals that \( f(n) = \frac{(n-1)!}{(n-4)!} \) for \( n \geq 4 \). Given the problem involves calculating products of such expressions, the solution simplifies to evaluating a telescoping sequence where most factors cancel out. Ultimately, the remaining product in the sequence is \( 2013! \), leading to the final answer: \( 2013! \).

Keywords

recursive function

telescoping sequence

factorial

product simplification

integer pattern