Consider a sequence so that an = the entries a1, a2, ..., a1000 are exactly 1 1 3' 3'4 except in a different order. Show that 1 -1,2' 2² n=1 (-1)" n 1 1000 an = Σ n=1 for n 1000, and so that (−1)n n

Q: PIUVE thlat Un 2 X9. A sequence {an} is defined recursively by ao = 1, a1 = 2, a2 = 24, and an = n 2…

A: The recursive relation has been proved in step 2.

Q: Show that the sequence defined by  a sub 1= 1  and  a sub n + 1 = 3 - (1/ a sub n) is increasing and…

A:

Q: Suppose that the sequence x, x1, x2... is defined by xo-1, x₁ =6, and xk+2=7xk+1-12x for 20. Find a…

A: Ans :

Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

A: The sales of dvds given as the function D = -0.92t + 8.75 and the total sales of streaming videos…

Q: 4. Define the sequence an by a, = 1, a, = 33, and an = 3an-1+ 10an-2 for n 2 3. Prove that an = 5" –…

A: Concept used :- we use mathematical induction to solve the given question.

Q: 1 for n 1,2,3 An An-1+an-2+an-3 for n >4 Prove that for n> 1, an < 2".

A: Given that an=1for n=1.2.3an-1+an-2+an-3for n≥4 The objective is to show that an≤2n for n≥1. Let's…

Q: 12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2,…

A:

Q: Find a closed form solution for the following recursive sequence: An = an-1+ 2" for n > 2 with the…

A:

Q: 1. Write out the next 4 terms of the sequence a = a,' +n-1; a, =1 (this means %3D а, а,, а,, а,).

A: Given a0=1 and an+1=an3+n-1a1 means n=0So, a1=a0+1=13+0-1          =0a2=a1+1=03+1+-1              =0

Q: Find an expression for the general term of the sequence: 4 7 10 13 - 3 9' 27' 81 3n + 1 O a,=(-1)"-…

A:

Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D

A: Here, the terms given in the series are, a1=0,a2=1an=n-1an-1+an-2 Calculate the third, forth and…

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&gt;Un…

Q: Show that the sequence delened by +5 mcreasing and ancg"for allkn an is thereas and anz9

A:

Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

A:

Q: 7. A. Determine the sum of the sequence Μ 3 Σ 10" n = 1

A:

Q: Write down the first five terms of the sequence an = 1 = 2 = 03 = 04 = 05 = (n + 5)! 7n²+6n +6

A: