Q4: (a) What is the general term an of the following sequence, assuming the sequence starts...
1. Determine an infinite sequence that satisfies the following ... (a) An infinite sequence that is bounded below, decreasing, and convergent (b) An infinite sequence that is bounded above and divergent (c) An infinite sequence that is monotonic and converges to 1 as n → (d) An infinite sequence that is neither increasing nor decreasing and converges to 0 as n + 2. Given the recurrence relation an = 0n-1 +n for n > 2 where a = 1, find...
Find a formula for the general term an of the sequence assuming the pattern of the first few terms continue 놀, 유 8 10 12 32' { 8 2 1 first term is a. Assume the first term an :
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. 5 5 5 5 20:37 2781
Write a formula for the general term an of each sequence for 4 of the following infinite sequences. a- -35, 34, -32, 29, -25, 20, ... b- 1, -1, 0.75, -0.5, 0.3125, -0.1875, ... c- 1, -0.5, 3, -0.25, 5, -0.16666666, ... d- 1/6, 1/4, 1/3, 5/12, 1/2, 7/12, ... show all the work please
5. Let {xn} and {yn} be sequences of real numbers such that x1 = 2 and y1 = 8 and for n = 1,2,3,··· x2nyn + xnyn2 x2n + yn2 xn+1 = x2 + y2 and yn+1 = x + y . nn nn (a) Prove that xn+1 − yn+1 = −(x3n − yn3 )(xn − yn) for all positive integers n. (xn +yn)(x2n +yn2) (b) Show that 0 < xn ≤ yn for all positive integers n. Hence, prove...
Question 1 3+cos(n) 2n X Which of the following properties hold for the sequence an for n 2 1? l. Bounded Il. Monotonic IIl. Convergent Selected Answer a. I only a. I only b. Il only c. I and Il only d. I and Ill only e. I, II, and III Remember what these conditions mean: Bounded means all terms of the sequence have to lie within a specific range of values. Monotonic means the sequence is ALWAYS increasing or...
show all work | 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing or monotone decreasing or neither? b) Find upper and lower bounds for the sequence. c) Does the sequence converge or diverge? (Explain) 3. Determine if the series converges or diverges. If it converges, find its sum. => [-1-] c) Ë ?j? – 1-1 j? +1
1. What does it mean for a sequence {a} to converge to a € R? State the definition. (-1)n+1 2. Prove that lim = 0 n 2n 3. Prove that lim +0n + 1 = 2 80 4. Prove that lim +-+V5n 9 - 7 5. Prove that lim 108 + 137 13
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
Write a formula for the general term an of each sequence a) -35, 34, -32, 29, -25, 20, … b) 1, -1, 0.75, -0.5, 0.3125, -0.1875, … c) 1, -0.5, 3, -0.25, 5, -0.166, … d) 1/6, 1/4, 1/3, 5/12, 1/2, 7/12, …