MathDB

1

Part of 2002 Putnam

Problems(2)

Putnam 2002 A1

Source:

3/12/2012
Let kk be a fixed positive integer. The nnth derivative of 1xk−1\tfrac{1}{x^k-1} has the form Pn(x)(xk−1)n+1\tfrac{P_n(x)}{(x^k-1)^{n+1}}, where Pn(x)P_n(x) is a polynomial. Find Pn(1)P_n(1).
Putnamcalculusderivativefunctionlimitcollege contests
Putnam 2002 B1

Source:

3/12/2012
Shanille O'Keal shoots free throws on a basketball court. She hits the first and misses the second, and thereafter the probability that she hits the next shot is equal to the proportion of shots she has hit so far. What is the probability she hits exactly 5050 of her first 100100 shots?
Putnamprobabilityinductionconditional probabilitycollege contests