how that the sequence (1 – (-1)" +1/n) is divergen

Q: The simple formula for a, if the first 5 terms of the sequence {an} are 1, 21, 121, 621, 3121 is:…

A: We are asked to find which is correct for the sequence.

Q: Write down the sequence whose nth term is (i) 2"/n and (ii) [3+ (-1)"]/3".

A: The main object is to write sequence for given nth term.

Q: What is a disadvantage of defining a sequence recursively?

A: The Disadvantage of defining a sequence recursively as In general, recursive functions are slower…

Q: limit of this sequence

A: We have to find out the limit of the given sequence.

Q: Find the sum of the first five terms of the sequence. (Assume that the sequence is defined for n ≥…

A:

Q: Find the 11th term of the harmonic sequence1/5,1/8/1/11,1/14,. . .

A: harmonic progression is 1arithmetic progression the given series has a pattern of = 13+previous term…

Q: A sequence {a„}1 satisfies a1 = 1, a2 = 1 and 6 an = max {an-1, an-2} – min {an-1, an-2} for n > 3.…

A:

Q: 25. Write the nth term of the sequence 2, 8/3, 32/9, 128/27... as a function of n.

A: Given,          2,  83, 329. 12827, . .  .

Q: Find the exponential generating function for the sequence 0!, 1!, 2!, 3!,...

A:

Q: Solve the following differential equation: (yesxy + x) dx + xes dy = 0

A: .To Find:Solve the above differential equation.

Q: Which of the following is the generating function for the sequence 5, 5, 5, 5 O A. G(x)=(1-x) 1 O B.…

A: Generating Function: Generating Function is a way to represent an infinite sequence. Consider a…

Q: a,=(- 1)" is a divergent sequence

A:

Q: The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777, ... is

A: The given sequence is 0.7,0.77,0.777,...... The sum geometric sequence with common ratio r<1 ,of…

Q: Suppose that the sequence {ak}1 is 2, 4, 6, 8, 10, 12, 14, 16, . What is a,?

A: we have the given sequence 2,4,6,8,10,12,14,16,...

Q: 7. Every sequence of real numbers has a decreasing subsequence. nondecreasing subse- quence or a

A:

Q: Need help with this problem. It states:   Determine the number of n-digit quaternary (0, 1, 2, 3)…

A: First, let's address the count of n-digit quaternary sequences where there is never a 3 to the right…

Q: Let {n} be a sequence. Let Yn = if {n} is monotonic, 1. Show that n then so is {yn}.

A: What is Monotone Sequence: A sequence can either be constant or monotone. There are two different…

Q: Find the first 4 terms of the sequence defined byf (n) = 1/2n+ n.

A: Consider a sequence an. The first n terms of the sequence are given by: a1, a2, a3,...an

Q: The sequence n-21 is divergent. True False

A: We have given a sequence  ,   n-2. We need to determine sequence is convergent or divergent. We know…

Q: f(n)=(n-1/2) (n-1/3) Its n-1 over 2 and n-2 over 3 Write the first six terms of the sequence…

A:

Q: Suppose that the sequence {ax} is =0 2, 4, 6, 8, 10, 12, 14, 16, .. What is a1?

A: The given sequence {ak}k=0∞ is -  {ak}k=0∞ = 2,4,6,8,10,12,14,16,18,......... The first tern of the…

Q: Suppose ao, a1, a2,... is a sequence such that ao = a1 = 1 and forn2 1, an+1 = n(an+an-1). Find az =…

A:

Q: 08. The sequence { GT) }n-1 3n+2 37+1

A:

Q: 12. (4 points) A sequence is given by the recursive definition an = An-1, +An-2 A0 = 1. a₁ = 1 and…

A: The objective of the question is to find the third term (a_3) of a sequence defined by the recursive…

Q: Evaluate the sum from k=0 to 4 of ((-1)^k(k+3)^2+3)

A:

Q: 6. Consider the sequence defined by the recursive formula an = 10 - a,-1 with ao = 2 (a) What are…

A:

Q: Find ai for the sequence with generating function, 1-x 1 x x

A: Simplify the generating function.

Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

Q: In step 3, how does (x+1)x! become (x+1)! in the denominator of the summation?

A: x!=x(x−1)(x−2)..........(2)(1)..................formula…

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.