MathDB

M365

Part of Kvant 2020

Problems(1)

Series of sum of cubes diverges

Source: Kvant Magazine No. 1 2020, 50th Anniversary, M365

3/10/2023
[*]The sum of several numbers is equal to one. Can the sum of their cubes be greater than one? [*]The same question as before, for numbers not exceeding one. [*]Can it happen that the series a1+a2+⋯a_1+a_2+\cdots converges, but the series a13+a23+⋯a_1^3+a_2^3+\cdots diverges?
real analysisConvergencedivergence