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1. Determine an infinite sequence that satisfies the following ... (a) An infinite sequence that is...
6. Give an example of a non-constant sequence that satisfies the given conditions or explain why such a sequence does not exist: (1) {an} is bounded above but not convergent. (2) {an} is neither decreasing nor increasing but still converges. (3) {an} is bounded but divergent. (4) {an} is unbounded but convergent. (5) {an} is increasing and converges to 2.
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...
would be nice if you could specify answers Question 12 A sequence {an}-1 satisfies a1 = 1, Q2 = 1 and 5 max {an-1,An-2} - min {an-1,An-2} 4. for n > 3. Select all what applies to the sequence {an}n-1 from the following list. (Remember: if a > b then max {a,b} = a and min {a,b} = b) (A) Alternating (B) Bounded above. (C) Divergent (D) Bounded below. (E) Monotonic. (F) 21005 (G) Diverge to o (H) 14 =...
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...
5 Consider the following continued fraction 2 + (i) Write the above continued fraction as the limit of a sequence. Also write a recurrence relation between the terms of the sequence. (ii) Show that the sequence is bounded. (i) Show that the subsequence of odd-indexed terms and even-indexed terms are monotonic. (iv) Show that the above continued fraction converges and find the limit. 5 Consider the following continued fraction 2 + (i) Write the above continued fraction as the limit...
1. Let {an}, be a sequence. Write down the formal definition of the following con- cepts. You have already seen some of these in lecture (a) The sequence is convergent b) The sequence is divergent. (c) The sequence is divergent to oo (d) The sequence is divergent to -oo (e) The sequence is increasing f) The sequence is decreasing (g) The sequence is non-decreasing (h) The sequence isn't decreasing (i) The sequence is bounded above (j) The sequence is not...
Polar Coordinate Problems 1. Identify when the function decreases when changing r2sin (29) = a(-1]b to coordinates Cartesian a = 1, b = 5 2. Draw the polar curve given byr = a (b + c cos (@)) in 0 s@sx/2. Find the arc length of that curve. a = 1, b = 5,C=-7 Sequences and series. For series, identify the method or technique to be used before applying it. If you are going to use root criterion, reason criterion,...
Problem 3 (10 points) Suppose a sequence satisfies the below given recurrence relation and initial conditions. Find an explicit formula for the sequence a -6a--9a,-2 for all integers k2 2 ao = 1, a1 = 3
1. Give an example of a convergent infinite series whose sum equals 1 Show that your series converges and show how to finds its sum (i.e. verify that the sum equals what we want). There are infinitely many possible answers! 2. n=1 3n2 – 2 (-1)" 4n5/2 + n a. Determine whether n=1 converges or diverges. 3n2 – 2 3n2 – 2 (-1)" 4n5/2 + n 4n5/2 +n b. Determine whether n=1 converges or diverges. 3n2 – 2 (-1)" 4n5/2...
Find the limit of the sequence if it converges; otherwise indicate divergence. n a. -sin 2n-1 Determine whether it is absolutely convergent, conditionally convergent, or divergent. Indicate the test used. (-1)tan 'n n° +1