olymmath

Putnam 2021 B2

  • Session B

Determine the maximum value of the sum S=∑n=1∞n2n(a1a2⋯an)1/nS = \sum_{n=1}^\infty \frac{n}{2^n} (a_1 a_2 \cdots a_n)^{1/n} over all sequences a1,a2,a3,⋯a_1, a_2, a_3, \cdots of nonnegative real numbers satisfying ∑k=1∞ak=1.\sum_{k=1}^\infty a_k = 1.

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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