MathDB

14

Part of 2007 Stanford Mathematics Tournament

Problems(2)

SMT 2007 Team #14

Source:

6/30/2012
Let p,qp, q be positive integers and let x0=0x_{0}=0. Suppose xn+1=xn+p+q2+4pxnx_{n+1}=x_{n} + p + \sqrt{q^{2} + 4px_{n}}. Find an explicit formula for xnx_{n}.
Sum of Differences

Source:

3/15/2010
Let there be 50 natural numbers ai a_i such that 0<a1<a2<...<a50<150 0 < a_1 < a_2 < ... < a_{50} < 150. What is the greatest possible sum of the differences dj d_j where each d_j \equal{} a_{j \plus{} 1} \minus{} a_j?