Putnam 1992 Problem A2 Let the coefficient of x 1992 in the power series (1 + x) α = 1 + αx + ... be C(α). Find ∫ 0 1 C(-y-1) ∑ k=1 1992 1/(y+k) dy.
Trivial. The usual Taylor series gives C(-y-1) = (y+1)(y+2) ... (y+1992)/1992! . Hence the integrand is simply the derivative of (y+1)(y+2) ... (y+1992)/1992! , so the integral evaluates to 1993 - 1 = 1992. Putnam 1992 © John Scholes jscholes@kalva.demon.co.uk 24 Dec 1998