A1.4

recognize, through investigation with or without technology, graphical and numerical examples of limits, and explain the reasoning involved (e.g., the value of a function approaching an asymptote, the value of the ratio of successive terms in the Fibonacci sequence) Sample problem: Use appropriate technology to investigate the limiting value of the terms in the sequence ${\left(1+\frac{1}{1}\right)}^1$, ${\left(1+\frac{1}{2}\right)}^2$, ${\left(1+\frac{1}{3}\right)}^3$, ${\left(1+\frac{1}{4}\right)}^4$, …, and the limiting value of the series $4\times 1-4\times \frac{1}{3}+4\times \frac{1}{5}-4\times \frac{1}{7}+4\times \frac{1}{9}-\dots$.