Question

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(4-9) Determine whether each series is absolutely convergent, conditionally convergent or divergent. Carefully show your work. 5 & 6) o sin 4k 8. 2 k=1 n= 1

Answer 1

tim antil z lim 16+14 qq no Tan I no loont Dil z lim intil 20 The series diveges, by Ratio test k-you lim lax 1 x = lim lk 175/6) = 1x5 = 56 s seves convergue absolutely by noot fest. an = buty 460) tim an=0 f'(n) = ln co whennai ? f decearing s By Leibnitz test, for alternating series, the sevics converger

Elanl = { 1 + > ERR { 2 > 1 and Et diverges. .. By Cempauson test s e direiges . The given series is conditionally convergent. 7 g (-3)kks k=1 (2k)! = lim (3) 2 + k +16 (26) K-70 (2k +2)! (3 tk. 1 alim k = 3 (k+1) a(k+1) QK+1) 0 .: lim (art1=0 By Ratio test the series converges absolutely.

8) Šo Sin (tb k=1 at I sink (< and  convergey since it is a geometric series with a r= 1 cl . By comparison test, since the bigger series converges smaller also does ole Binak converges absolutely Kai ham lan Mo lim By Roof best, series diverger. .! The series diverges.