Question

∑sin π/k
converge or diverge? please attach you worksheet.

Answer 1

doh!! and i was wrong lol

http://www.wolframalpha.com/input/?i=%E2%88%91sin+%CF%80%2Fk

Answer 2

i shoulda went with my first guess.... lol

Answer 3

Nice 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.