Consider the alternating series 116 Kn+3)! n=15 n=15 and the following propositions: 1. lim an = 0 II. an+1 < an, Vn > N with NEN With certainty, it can be guaranteed that: a) Both propositions are true b) Both propositions are false c) Only proposition I is true Only proposition II is true

Q: Consider the equation where x1,x2,...,x9 € N. How many solutions are there if: a) b) c) Xi 9 for all…

A: As per the question we are given a linear equation : x1 + x2 + ... + x9 = 73 And we have to find the…

Q: choose all correct answers: 1)proof is wrong 2) proof is correct. 3) the base case is incorrect…

A: Mathematical induction: Mathematical induction could be a methodology of proving that a press…

Q: 2. Use a matrix to determine if the set a1, a2, az is linearly dependent or linearly independent. If…

A:

Q: 2.2.6 Consider the following proposition, where x is assumed to be a real number. x3 – 3x2 – 2x+6=0…

A: We have to consider the proposition where x is a real number x3-3x2-2x+6=0 implies that x=3  a) We…

Q: A bag contains 17 marties 7 red, 7 green and 3 blue. In ths experment, 8 martles are taken out of…

A: Classical Definition of Probability: If there are n mutually exclusive, exhaustive and equally…

Q: Q: If a,,a,, aza,. are in A.P. such that a, +a, + ao + as + az0 +a24 = 450 Then find the sum a, + az…

A: Given: a1, a2, a3, a4, .....  are in A.P.  such that:a1+a3+a10+a15+a20+a24=450

Q: 3. If 2" – 1 is prime, then n is prime. 4. Let x be a real number. If x > 0, then > 0.

A:

Q: root of 25 is 6". wing questions with either T (if true) or F (if false

A: the statement p: 8 mod 2 =1 since 2 divides 8 therefore 8 mod 2 =0≠1 (a) therefore the truth value…

Q: 2 3 n a. If n E N, then + + + •+ 3! 4! (n+1)! (Hint: 3! (reads 3 factorial) = 3 x 2 x 1. n! = nx…

A: Induction theory: Let the given statement is P(n). Step-1: We need to check P(n) is true for n=1.(or…

Q: {15n : п € Z} %3 {3п :п€ Z}n{5n :n€ Z}

A:

Q: a) If 4x1 = 4 mod 9 and 0 < x < 9, then x = b) If 70x + 19 = 0 mod 141 and 0 ≤ x < 141, then x = c)…

A: a) If 4x-1≡4 mod 9 and 0≤x&lt;9, then x= . b) If 70x+19≡0 mod 141 and 0≤x&lt;141, then x= . c) If…

Q: け) Let A and B be A=/132 1-2- 132 926 Find elementary motria E such that EA=B

A:

Q: 5) Y = is prime id eal D Truel O Fulse

A: Statement y=&lt;5&gt; is a prime ideal. To determine whether the given statement is true or false.

Q: 1. For an autonomous differential equations, it is possible to view all of the solution function gr…

A: 1 Answer:- The given data. a The representative graphs of solution.→ The given data - y = 0 y = 0→…

Q: Prove NIn, +oo[= 0 ! n=1

A: To prove that ∩n=1∞[n,∞)=∅. Suppose that x∈∩n=1∞[n,∞). Then, x∈[1,∞), x∈[2,∞),.... That is, x≥n,…

Q: The number of 3-permutations of 5 objects with repetition allowed is 51 / (5-3)! 35 5x3 53

A:

Q: 7. Prove that if n² is a multiple of 6, then n is also a multiple of 6. [Hint: Consider residues…

A: To solve this problem we use the following theorem  Theorem : p and q are distinct primes such that…

Q: X1) Use the following statement to answer each of the following questions. "For any integer n2 2, if…

A: Given the statement, "For any integer n≥2, if n is composite (not prime), then there is a factor k…

Q: 10. Prove the following identity 2 n+1 k=1

A: To Prove - ∑k = 1nn - 1k - 12n - 1k-1 = 2n + 1       Formula used - ab = a!b! a-b! where a! =…

Q: The elements of P({a, b, {a, b}})= 10, * .where a and b are distinct elements true False O

A:

Q: Consider the statement If n is even, then 4n² - 3 is odd. The contrapositive of the given statement…

A:

Q: general berme 67 Study the sequences of the general. un = exp(-un-1) with to given Un = √un-1 -…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: What is the mode of the series below? Aşağıdaki serisinin modu kaçtır? Class Frekans 10-13 2 14-17 4…

A:

Q: A popular lottery game is one in which two digits from 0 to 9 are chosen so that the winning number…

A: A popular lottery game is one in which two digits from 0 to 9 are chosen so that the winning number…

Q: n² < 2" for n = 4,5, 6, ... (Hint: 2n + 1 < 2" for n = 3,4, 5, ...)

A:

Q: Dice You roll a fair die three times. What is the probabil-ity that a) you roll all 6’s?b) you roll…

A:

Q: Number of circular permutations of different things taken all at a time is n! a.) True b.) False c.)…

A: If n is the number of circular permutation of n different things taken all at a time, then the total…

Q: Consider If 25* 11* = 4 mod 3, find x. 25 = 1 (mod 3) and 11 = 2 (mod 3),

A: a≡bmodmc≡dmodm⇒ac≡bdmodm

Q: Consider the following: Claim: For all n E N, (*) D-1 i = (n+)* %3D Proof: We prove the claim by…

A:

Q: 8) Find the nh term of the following sequences 1 1 1 8. 1 1 а) 2 4 16 32 b), 2 4 8 16 25 125 625 c)…

A:

Q: 8) Which statement describes the decimal equivalent of ? 8. A. It is a decimal with a repeating…

A: To find: Which statement  describes the decimal equivalent to 7/8

Q: Consider the succession (an) To=18 an = 170an-1-5929an-2, n ≥2 defined by land a₁ = 1674. 7.1)…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…