text: cos kw/k is real part of \n\n(e^i(kw)/k)\n\nbecause\n\ne^ix = cos x + i sin x\nhence sum is real part of\n\nsum ( e^i(kw)/k\n\nthe above is less than the term e^&#92;(ikw) which is geometric series\n\nthe series diverrges when e^i(kw) = 1 for all k else it converges\n\nfor the case e^ikw = 1 \nwe get 1+1/2+1/3........... this diverges\n\nfor others it converges\n\nwhen cos w = +/- 1 or w = npi divergent\nfor other w convergent