EXAMPLE 8, Does the sequence whose nth term is n п + An n 1 - converge? If so, find lim,»oan.

Q: -n +1 lim -n2 +n +2

A: Given to find limn→∞-n2+1-n2+n+2n

Q: For the sequence { 4^(-n) } a) determine whether or not is convergent b) if it is convergent,…

A: The nth term of the given sequence is given by bn=4-n. If limn→∞bn exists, the sequence bn is…

Q: Whst is the exact value of the limit of the sequence (7^(n+1)-7)/7^n?

A:

Q: Determine whether the sequence is monotonic and whether it is bounded. sinyn an

A: It is required to check whether the given sequence is monotonic and bounded.

Q: What is the exact value of the limit of the sequence -n^3/(n^4+1)?

A: To determine the value of the limit.

Q: 3. What is the 10th term of the sequence whose nth term is an = (n^2+2n-3)/(n+1) ? * O 117/11 O…

A: We are given the nth term of the sequence and we need to find the tenth term of the same. This can…

Q: Q1/ Isthe sequence {a,} converge ? († - ) -

A: If a sequence converges to some limit, then it is convergent; otherwise it is divergent.

Q: 4n2 Determine if the sequence {an}I with an= converges. If it converges write its limite if it…

A: Given Data The sequence formula an is:     The expression for the limit of sequence an is,

Q: Find the limit of the sequence defined by an (Hint: apply L'Hospital's Rule. 2" Be careful in…

A:

Q: A sequence can be generated by using a_(n)=a_((n-1))+4. If a_(1)=2, what is the value of a_(20).

A:

Q: prove that the sequence (1/5^n) is convergent and approaches zero?

A: Series and sequences

Q: The sequence fn is given asf1=1 ,f2=3 ,fn+2=fn+fn+1 for n>_ 1. How many even terms are between the…

A: Calculate first few terms of the sequence, by substituting, n=1,2,3,... in the equation,…

Q: For each infinite sequence, find the limit, or determine that the sequence diverges.…

A: Divide the numerator and denominator by k

Q: List the first six terms of the sequence defined by\[a_{n}=\frac{n}{2 n+1}\]Does the sequence appear…

A: The given sequence is: an=n2n+1. To Do:List the first six terms of the given sequence. Check whether…

Q: Let (a_n)be the sequence defined by the recursive relation a_n=na_(n−1), with initial term a0=1.…

A: Given that:  an=nan-1               a0=1

Q: Show that the sequence $a_{n}=\frac{n}{n^{2}+1}$ is decreasing.

A: The given sequence an=nn2+1. We have to show that the sequence is decreasing.

Q: For what values of $r$ is the sequence $\left\{r^{n}\right\}$ convergent?

A: The given sequence rn. We have to find the values of r such that the sequence is convergent.