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42. Let (an) be the sequence defined by ao (0,Vn2 1, an+1 = sin(a,) T 1 1 (a) Show that lim nan (b) Deduce the nature of the
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42. Let (an) be the sequence defined by (o) sin(an) n 1, an+1= 1 1 Yaj Show that lim na 3 b) Deduce the nature of the seriesNow V. sin lim sin 2-2 sinx Cos a im R 2 sinx CoS T 2X Sin ol (2x) 2. Co S 2 im - 2x + 22 Sm22 t 2sinx 2. Si 21 CoS 2 cos2x4 CoS2 Lim Cos2X + 8 C0S2K 4 Sim 22 -4 -(6xsin2x +4 Cos2x 4 3 2.Thus lim 3 using if (an) is a sequence for which them lim (an+1 an = a noo then an lim noo n = a. have υue Lim 3Κανε From 3 which eleary mde eates thak Σ is an Comparison by he est

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