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.
The 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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