Question

Α. ω πλεον εως 18 Σ. και Σ. καντηριο THEN Σ. απαντού και ΠΟ (0) Cretudo that IHΣH - - Ε τΗεΝ Σ (e) Give a counterexample to the following FALSE statement: IF a, converges THEN azn converges and a2n+1 converges. n=0 O

Answer 1

Date Date ___ Page - Page 6.4 Given that Zazn and Z aant) converges no where aan= lot azt auta, t - - - - S n=0 and aan+1 = a, tast astant- (3 n =D Noro from 29+3 Z aan no = + Zaznti n =d a + at azt azt autag tag tagt - - - Zan » Žan = Z azn + Zant ΥΞo n = 0 n =0 e Let 2 azn=s and 2 aantat no then to ana s tt n=0 mi02 → San is convengoo, nzo

6 Given that if ne) Nino Cosider > s= a + (s) - s= π + S > S- S - T s T 12 227

Dale Page but oo z azn = n=a o an ==Ź - + -- =-(² + 1 + 1 + -) Y- Hences diverse sequence G - n=0 . . £ (1) ip diverse. n= and dant)= n-o ntl - Ķ + + = + = + --- also diverse sequence. is

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