Mathematical and Physical Journal
for High Schools
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Problem A. 520. (November 2010)

A. 520. Is there any infinite sequence a1,a2,... of nonnegative numbers for which \sum_{n=1}^\infty a_n^2 is finite and

\sum_{n=1}^\infty \bigg(\sum_{k=1}^\infty\frac{a_{kn}}{k}\bigg)^{2} = \infty?

(Miklós Schweitzer Competition, 2010)

(5 pont)

Deadline expired on December 10, 2010.


4 students sent a solution.
5 points:Nagy 235 János.
0 point:3 students.

Problems in Mathematics of KöMaL, November 2010