Question

1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating. (b) 1/2-1/4+1/6-1/8+1/10-..... converges conditionally. A convergent sequence is always Cauchy. {1/n) is a Cauchy sequence. (1-3)-(1-31/2)+(1-313)-(1-314 )+.....diverges. 2. Find limit sup and limit inf of the following sequences: (10 pts) (a){c+4) sin ng (b) {(1+m+)"} Limsup= limsup= Lmitinf= liminf= 3. Prove that either the following sequence has a limit or not. (20 pts) (a) 2n (b) n2+4n+2 n+6vn n-1

Question 1 please

Answer 1

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