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anonymous
 5 years ago
∑sin π/k
converge or diverge? please attach you worksheet.
anonymous
 5 years ago
∑sin π/k converge or diverge? please attach you worksheet.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0doh!! and i was wrong lol http://www.wolframalpha.com/input/?i=%E2%88%91sin+%CF%80%2Fk

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i shoulda went with my first guess.... lol

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Nice problem! :D Notice that geometrically, the line passes through (0,0) and \((\pi/2,1)\) lies below the graph of \(\sin x\) on the interval \([0,\pi/2]\). Hence on that interval we have \[\frac{2}{\pi}x<\sin x\] It follows that for \(k\geq 2\) we have \(2/\pi \cdot \pi/k<\sin (\pi/k)\), i.e \(2/k<\sin(\pi/k)\). But since \(\sum 2/k\) diverges, then \(\sum \sin(\pi/k)\) diverges as well.
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