8. (a) Give an example of a convergent sequence (s) of positive numbers such that lim (s/s) 1. (b) Give an example of a divergent sequence (1) of positive numbers such that lim (1/1) 1.
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- A sequence is a function whose domain is ____________.Please give an example of a sequence (an) that has: (a) an(k) = (1/k) as a subsequence where n(k)= 3k. (b) an(k) = ((-)^(k)k^(2) as a subsequence where n(k)= 2k -164. (a) Determine whether the sequence defined as follows is convergent or divergent: a1 = 1 an+1 = 4 – an for n> 1 (b) What happens if the first term is a = 2?
- 16. (a) Give an example of a convergent sequence (x,) of positive numbers wich lim(x/x,) = 1. (b) Give an example of a divergent sequence with this property. (Thus, this property cannot be used as a test for convergence.)Consider the sequence an = +3" 4" (a) Is the sequence monotonic or non-monotonic? If it is monotonic, determine if it is decreasing or increasing (show your work). (b) Is the sequence bounded? If it is bounded, find its boundaries. (c) Is the sequence convergent or divergent?approximate Jio what ir the appopriate upelate rule for the Sequence Xn To using Newton's methoel,
- Consider the sequence P,-=(0.3)*" the the order and the asymptotic error constant when the sequence converges to 0 are respectively: Select one: a. 3 and 2 b. 2 and 3 C. 4 and 1 d. 3 and 1 Previous page Next page chGive an example of a sequence (an) and (bn) such that (an) and (bn) diverges and (anbn) converges. I know how to do it but my teacher used an= 1/n as the converging sequence claiming that it goes to 0?? Isn't it a diverging sequence?? Like his answer was an= 1/n and bn=n so if you multiply them it's 1.Write out the first five terms of the sequence, determine whether the sequence converges, and if so, find its limit 1 (e) +00 {*}}
- Assume that the sequence shown below converges and find its limit. V8. /8+ /8. /8+ J8 + /® , /8+ /8+ /8+ vo ... The sequence converges to lim an (Type an exact answer.) IIlimit of the sequence lim h→∞ (1+2/h)^h1, 1/(1-1/2), 1/(1-2/3), 1/(1-3/4), ... Show steps please: Find an explicit formula an = ---- for the sequence and explain whether it converges or not. If it converges, find limn->oo an