Question

2. (BASIC] Basic concepts of sequences. Do BOTH of the following. • Consider the sequence What can you say about this sequence? (CIRCLE ONE) – The sequence CONVERGES to - The sequence DIVERGES (i.e. the limit does not exist as a number). Then EXPLAIN why you answered as you did. • A sequence is given by ao = -2, and for n > 0, Ant1 = V6an + 16. (a) Give aj and a2 to the nearest THOUSANDTH. (b) Assuming that the sequence has a limit L, what must L be? EXPLAIN.

Answer 1

ince . . . 1- 21 = 4 4 2 (-2) Converges to : o. Now, let Exo. Then if tal, let no=1. Then, 1(-) - 0 <¢ for all nano So let OCELI. Then, 4, +<1 implies that rog 13 log € <0. and hence logt So, for - Now so, OLECI 163) Ofec (2) CE » n log & <loge if a co, ablaca byci no loge slog Let no a 1 T dogt - Togų | Then for no 1999-01 <t, bino 1 Thus, for any fo we can find an positive integer no such that 1633901 <e for ak si z no. Thus, (-42) n converges to oi idaman • Given ao=-2 and for não, anti=V6 an +16 (a) a = √600 + 16 = √6. G-2) +16= √-12+16 = 54=2. A2=/Gat 16 = √6.2+ 16 =√12+16 = √28=5.292 Rounded off to nearest THOUSANDTH.]