Does ∑n≥0 n! kn/(n + 1)n converge or diverge for k = 19/7?
The nth term divided by the n-1th term is k n nn-1/(n+1)n = k/(1 + 1/n)n which tends to k/e. But k/e < 1, so the series converges by the ratio test.
5th Putnam 1942
© John Scholes
5 Mar 2002