Maximizing the sum \(\displaystyle{\sum_{{{n}={1}}}^{{m}}}{\sin{{n}}}\) For which value of

Axel Stout

Axel Stout

Answered question

2022-04-13

Maximizing the sum n=1msinn
For which value of m, we will obtain the maximum sum?
Here's my approach : n=1msinn=sin14sin2122cos(m+12)4sin(12)
If we can minimize 2cos(m+12) then this will result in maximizing the sum.
But the problem is I can't quite figure out what the minimum value of cos(m+12) is.

Answer & Explanation

awalkbyfaithbzu6

awalkbyfaithbzu6

Beginner2022-04-14Added 21 answers

There is no value m which solves your conditions.
For a maximum we need m=π(2k+1)12N which is not possible for any kZ
The supremum for the sum is sin14sin212+12sin(12)

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