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Prove that for every natural n the following inequality is valid:
|sin 1| + |sin 2| + |sin(3n-1)| + |sin(3n)| > 8n/5.
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Surely it's not?
You've got 4 sin functions on the left, and each individual term is never >1, which means that the left side is never >4.
Setting n=5 makes the right side become 8 and so the inequality is false.
Why did the vector cross the road?
It wanted to be normal.
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