For r E N*, let a, be the number of integer solutions to the inequality x1 + 22 + x3 + x4

Q: The limit of the sequence (극n(n2+ 1)-In(2n + 1마- Select one: а. 1 8 b. In2 C. - In2 d. -2 e. None of…

A:

Q: Determine the number of integer solutions for x₁ + x₂ + x3 < 33 where x, 72 X2 2-1 and - 1 ≤ x₂ <19

A:

Q: If there are two numbers, b and c such that 2b’s and 5c’s sums to 8.  Maximize the product of b and…

A:

Q: (a) How many nonnegative integer solutions are there to the equation ₁ + x₂ + x3 + x₁ = a? (b) How…

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: Matching: 1. Geometric Sequence 2. Quadratic Function Standard Form 3. Function Composition Rule A.…

A:

Q: 1. Find the number of zeroes at the end of 100!

A: Introduction :Here, we have asked for the number of zeros at the end of 100 !

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: B1. Is the sequence (a,} where a, =-n+3 a solution of the recurrence relation a, -1+2a,-2+2n-9. B2.…

A:

Q: Sequence hWith frst tem 7, and las term 7/729.

A:

Q: The partial sum - 2 + (– 8) + (– 32) + + ( – 512) equals

A:

Q: A sequence bo, b1, b2, ... is defined by letting bo = 5 and b = 4+bk-1 for each integer k> 1. Show…

A:

Q: 3. Is the sequence defined by a = 2(-4)" + 3 a n solution of the recurrence relation a = -3 a +4a n…

A: Given Data:  To check the sequence 2-4n+3 is a solution of recurrence relation an=-3an-1+4an-2.

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: a. Use the appropriate formula to determine the periodic deposit. b. How much of the financial goal…

A:

Q: of all positive integers Find the sum less than 200

A:

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: show that the general factorial function: () (¹) (+).. m (a)m here m is a positive integer and n is…

A: Given Data: To show that the general factorial function  αmn=mmnαmnα+1mn.........α+m-1mn here m is a…

Q: Show that 2n+1≤2^n  for all n≥3.

A:

Q: Suppose An = 2n^2 + 6n + 6. Find the closed formula for the sequence of differences by computing An…

A: As per our question, we need to find the closed form of an-an-1×an-an-1 First find an-1 and then…

Q: 14) Show that f (æ) = -æ³ +2 is decreasing on the entire real number line. (Show Graph)

A: we have to show that the given function is decreasing and also draw the graph of f(x)

Q: Is 103= 58 mod 5 true or false?

A: Note: a mod b is the remainder from the division of a by b. Given: 103 = 58 mod 5.

Q: Use the method of finite differences to find a closed polynomial formula for the following sequence…

A: 1, 3, 21, 91, 273, 651, 1333, 2451, 4161, 6643,... find the first difference D1=2,18, 70, 182,…

Q: If the arithmetic mean of two unequal positive real number 'a' and 'b’, (a > b), be twice as great…

A:

Q: Is a product of two positive decimals each less than 1 always less than each of the decimals?

A: To state the give statement is true or false.

Q: 4. Find a number 8 >0 such that if Ix-10] < & then |(2x + 3)-23|< 0.25.

A: I am going to solve the problem by using some simple calculus to get the required result of the…