Mark each statement as TRUE or FALSE. If lim a,=0, then an converges. n- 00 n=1 True False If an converges, so does lanl. n=1 n=1 O True O False If la,l s 3-n for all n, then an is convergent. n=1 True False If { a, } is a decreasing sequence, then lim a, must exist. n- 00 O True O False

Q: 6. Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence…

A: We have to examine the given sequence abouts its property

Q: (-1)"n en

A:

Q: determine the limit of the sequence or show that the sequence diverges.

A:

Q: 10. Let an be a sequence of reals, and be a real. Let bn = lan-ll. Show that an converges to & if…

A: Given a sequence of real numbers an and l is a real number, given bn=an-l.   If a sequence xn…

Q: 2. Give an example of an unbounded sequence {an} of negative terms such that an does not diverge to…

A:

Q: Determine if the following sequence converges or diverges. an = -10(n!) (-8) Note: If it converges,…

A: Given: an=-10n !-8nTo check: Whether the sequence converges or diverges.

Q: 1 2n+3 - whether an C. Is the sequence bounded? is increasing, decreasing or not

A: a sequence {a_n} is called bounded if there exists two real numbers m and n such that…

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A:

Q: 3. Consider the sequence defined recursively by 3 90+1=1 (0+²) an+1 (an an 2 an (a) Write the terms…

A: In this question, we will find the first six terms of the sequence and the limit of the sequence.

Q: Find the limit of the sequence; {an}n21 if: 1+2/2+3/3+.+n/ñ An choose one alternative as an answer:…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.