Sum the series below:
[MATH]\sum_{n=4}^{999}\dfrac{1}{\sqrt[3]{n^2-2n+1}+\sqrt[3]{n^2+2n+1}+\sqrt[3]{n^2-1}}.[/MATH]
Question 1: Do you think the expression on the denominator can be factored?
Yes.
No.
This is a really rich way to asking problem so we make the students to think deep before simply giving out the answer yes or no so easily.