MathDB

B4

Part of 1946 Putnam

Problems(1)

Putnam 1946 B4

Source: Putnam 1946

3/13/2022
For each positive integer nn, put pn=(1+1n)n,  Pn=(1+1n)n+1,  hn=2pnPnpn+Pn.p_n =\left(1+\frac{1}{n}\right)^{n},\; P_n =\left(1+\frac{1}{n}\right)^{n+1}, \; h_n = \frac{2 p_n P_{n}}{ p_n + P_n }. Prove that h1<h2<h3<…h_1 < h_2 < h_3 <\ldots
PutnamSequencesapproximation