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Suppose the sum \[\sum_{n=1}^\infty \left[ H_n - \gamma - \ln n - \dfrac{\zeta(2n)}{2n} \right]\] can be expressed in the form ...

Beginning with a square of area 1, construct a sequence of rectangles by alternately adjoining a rectangle of area one alongside or on top of the previous rectangle. First five ...

Diagonals of a regular 30-gon

Let \(M_n\) be the arithmetic mean of the lengths of all the diagonals of the regular \(n\)-gon with a circumradius of \(\pi\).

Compute ...

Which is closest to \(\cos(22)\)? (The argument is in radians.)

Hi Brilliant! This is the sequel of the first part of Brilliant Summation Contest Season-1.

Update: This contest has been ended. Thanks for everyone's participation.

The aims of the ...

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