MathDB

B2

Part of 1949 Putnam

Problems(1)

Putnam 1949 B2

Source: Putnam 1949

3/20/2022
Answer either (i) or (ii):
(i) Prove that ∑n=2∞cos⁡(log⁡log⁡n)log⁡n\sum_{n=2}^{\infty} \frac{\cos (\log \log n)}{\log n} diverges.
(ii) Assume that p>0,a>0p>0, a>0, and ac−b2>0,ac-b^{2} >0, and show that \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \frac{ dx\; dy}{(p+ax^2 +2bxy+ cy^2 )^{2}}= \pi p^{-1} (ac-b^{2})^{- 1\slash 2}.
Putnamlogarithmsdivergence