8

Part of 2006 Stanford Mathematics Tournament

Problems(3)

Addition and Multiplication Swapping

Source:

Given two 2's, "plus" can be changed to "times" without changing the result: 2+2=2·2. The solution with three numbers is easy too: 1+2+3=1·2·3. There are three answers for the five-number case. Which five numbers with this property has the largest sum?

2006 SMT Algebra #8 - Evaluate

Source:

\sum^{10}_{x=2} \dfrac{2}{x(x^2-1)}

2006 SMT Team Round #8 - Evaluate

Source:

\lim_{n\rightarrow\infty}\sum_{k=n^2}^{(n+1)^2} \dfrac{1}{\sqrt{k}}