## Le Monde puzzle

The puzzle in Le Monde is quite straightforward (!) this weekend: it can be rewritten as to figure out the values of the sums

and

which are easily displayed and as easily solved.

**T**he first sum can indeed be written as

for . This is simply

and the solution is thus , equal to -1 for . Once we realise the fact this is a product with one missing term, the second sum is similar: it can be written as

This is equal to 1 for . A bit disappointing because it amounts to reformulate the question with the proper algebraic formula…

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