Consider the infinite sequence of shaded right triangles in the accompanying diagram. Compute the total area of the triangles. 1 -l00 -|0 -IN -IN

Q: Suppose we have the sequence 5, 5/9, 5/81, 5/729, ... Find an explicit formula for the nth term of…

A: Given Data: Sequence: 5, 5/9, 5/81, 5/729 Check common ratio for a geometric sequence. The common…

Q: Find the limit of the sequence with the given nth term.  an = 6 + 2/n2

A: Given sequence is an=6+2n2. If ∑n=1∞an converges, then limn→∞an=0.

Q: Determine whether sequence having the given nth term is monotonic           an = 3 + (−1)n

A: an = 3 + (−1)n We need to determine whether the sequence having the nth term is monotonic or not.

Q: Find the limit of the sequence with the given nth term. n + 5

A: Given sequence is an = (n+5)/n

Q: bn Уп? + 6п — п,

A: Given that the sequence bn=n2+6n-n where n∈ℕ and ℕ is the set of natural numbers. We have to…

Q: Write an explicit formula for an, the nh term of the sequence 5, –1, –7,.... -

A:

Q: Use the rules for sums of powers of integers to compute the sum. 16 Σ k k=7

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Q: Find the limit of the sequence with the given nth term. n + 6 n

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Q: Evaluate the limit of the sequence or state that it does not exist. an = (8n)/(n!)

A:

Q: (2) Give the infinite sum definition of e using factorial numbers. e Please don't forget at the end.…

A:

Q: Find the limit of the sequence with the given nth term. 5n + 7 5n

A: we have givenan =5n+75n

Q: of the first 100 terms of the sequence: ; 99 Find the sum ak k=0

A: Given that, an=6+9n We need to find the sum of the first 100 terms of the sequence ∑k=099 ak

Q: Write an explicit formula for an, the n'n term of the sequence 1, 5, 25, ... .

A:

Q: Suppose that a sequence is defined as follows. a=2, a,=-3a,-1 for n22 List the first four terms of…

A: Given :              a1 = 2              an = -3 an-1 + 5 To find :                    The first…

Q: Find the limit of the sequence with the given nth term an = (n + 1) /n

A: an = (n + 1) /n We need to find the limit of the given sequence.

Q: Find the limit of the fallowing sequence if it exists 92 = 12-2, an =/2-/2+12+2+..+2 ' n eN

A: Explained below

Q: Given a sequence defined by the explicit definition: tn = 2" – n, find the 5th term of the sequence.…

A: It is given that,the sequence:tn=2n-n We have to find the 5th term of the sequence.

Q: For the sequence, find a number k such that n'a, has a finite non-zero limit 5n? + 3n +4 a. 4n° +…

A: Given that an=5n2+3n+44n4+2n+2n8 Take n2 in the numerator and n4 in the denominator. Then we get,…

Q: Use the rules for sums of powers of integers to compute the sum. 19 Σ 4.² k=6

A:

Q: Consider an infinite sequence of circles as in the diagram. What is the sum of the areas of all…

A: This is a problem on infinite geometric progression which is solved as shown below.

Q: Write a formula for the nth term of an of the sequence and determine its limit (if it exists).…

A: The sequence is: 1, -22, 34, -48, 516, ..... This can then be written as:

Q: Use the rules for sums of powers of integers to compute the sum. 17

A: Given : the summation of k2, k from 3 to 17.

Q: Evaluate the limit of the sequence or state that it does not exist. an = (-1)n (3n3 + 4n)/(6n3 + 5)

A: Given sequence: an=(-1)n(3n3+4n)(6n3+5) To find the limit of this given sequence:…

Q: Find the limit of the sequence with the given nth term. an = n + 3/n

A: We are given

Q: Use iteration to guess an explicit formula for the sequence defined by an = an-1 + n for all…

A:

Q: Determine whether sequence having the given nth term is monotonic           bn = 2n /(1 + n)

A: Given sequence is bn=2n1+n A sequence is monotonic if it either increasing or decreasing through out…

Q: Find the limit of the sequence as n approaches infinity: In – 8 an = 9п + 1

A:

Q: Evaluate the limit of the sequence or state that it does not exist. an = (3n3 + 4n)/(6n3 + 5)

A: To calculate the limit of the sequence limn→∞an, divide the numerator and the denominator of the…

Q: Find the limit of the sequence or determine that the limit does not exist. n! an= 4n.7n

A: Consider the given sequence, an=n!4n·7n

Q: A sequence {an} is called monotonic, if it is neither increasing nor decreasing. Select one: O True…

A: False.

Q: For the sequence defined by: ai = 2 1 + 5 An аn + 1 — Find: a2 az = a4 = II

A: To find  a2 , a3 , a4  substitute n=1,2,3 respectively  in the given equation.

Q: Use the difference an+1-an to show that the sequence {n-9"} is strictly increasing or strictly…

A:

Q: Find the limit of the sequence with the given nth term.

A: To find the limit of the sequence whose nth term is an=6+2n2

Q: Use the rules for sums of powers of integers to compute the sum. 21 Σ k k=3

A:

Q: Find the limit of the sequence with the given nth term. 3n + 4 a in 3n

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Q: 2" An 2n+1

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Q: Determine if the sequence is monotonic and if it is bounded. n! 5n

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Q: Find the eigth term of a sequence 3,6,12

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Q: Find the limit of the sequence: In? + 2n + 2 9n2 + 5n + 3 Question Help: Video Message instructor…

A: We can use limit in order to solve the given problem.

Q: the n^th term of the following sequence 1,4,7,10,...is

A: For given sequence a1 = 1 a2= 4 a2 = a1 + 3

Q: determine whether the sequence is incraesing ,decresing or not monotonic . isthe sequene bounded…

A: Given,

Q: Find the limit of the sequence with the given nth term. Зп + 8 an 3n

A:

Q: Determine if the sequence is monotonic and if it is bounded. (2n + 8)! an n21 (n + 4)! '

A:

Q: Consider an infinite sequence of circles as in the diagram. What is the sum of the areas of all…

A: To find: The sum of areas of the circle: Formula used: Area of the circle is  A=πr2 The sum of…

Q: Find the sums given (a) 2k k31

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: does this sequence coverage? ∞ Σ         (arctan * n)/n n=1

A: By limit Comparison Test , Series is Divergent

Q: Write an explicit formula for a_nan​, the n^{\text{th}}nth term of the sequence 2, 4, 6,

A:

Q: For the sequence defined by: a1 = 3 5 an+1 = an +1 Find: a2 = Preview az = аз Preview a4 = Preview

A:

Q: Find all the terms of the finite sequence. 6) an = n²-n for 1≤n=5

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Q: Find the limit of the sequence. 3n2 an n2 + 9

A: an=3n2n2+9 if limn→∞an=L then the sequence is converges if limn→∞an=∞ then the sequence is diverges…