10

Part of 2006 Stanford Mathematics Tournament

Problems(4)

Source:

What is the square root of the sum of the first 2006 positive odd integers?

2006 SMT Algebra #10 - Evaluate for |a|<1

Source:

\sum^{\infty}_{k=1} \tfrac{k}{a^{k-1}}

|a|<1

ratiogeometric sequence

2006 SMT Team Round #10 - Smallest Positive m

Source:

Find the smallest positive

m

for which there are at least 11 even and 11 odd positive integers

n

\tfrac{n^3+m}{n+2}

algebrapolynomial

Σ with Trigonometry

Source: 2006 SMT Advanced Topics Test Problem 10

Evaluate: \sum\limits_{n\equal{}1}^\infty \arctan{\left(\frac{1}{n^2\minus{}n\plus{}1}\right)}

trigonometrylimit