2. Let, a1 = 3 and for n > 2, an 2an-1+1, express an in terms of n.

Q: Write out explicitly and simplity possible as h= 5 n!

A: ∑n=0n=5 n2n!=?

Q: Let n and m be positive integers. Evaluate >(km+1 – (k – 1)m+') if possible. If not possible, k=1…

A: Write the terms one by one and add them.

Q: What statement could be used to prove that m f n?

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Q: 3. Find the number that provides a counterexample to show that the given statement is false. a) For…

A: Hi, thank you for the question. Since you have posted multiple questions with multiple sub-parts, as…

Q: Suppose X= N(10, 1.924)Pr(9.65 is less than or equal to X and X is less than or equal to 12.7)

A: Given a normal distribution with mean 10 and variance 1.924.the relationship between standard…

Q: 3. Let n and m be positive integers. Evaluate > (km+1 (k – 1)m+1) if possible. If not possible, k=1…

A: We have to evaluate the given summation.

Q: 2- Show that: (-1)m (2m + 1)! NIE

A: Solution:     Definition of Bessel's function:

Q: Let n € Z. Prove that if 2 | (n² – 5), then 4 | (n² – 5). Solution:

A:

Q: 2. Let, a1 = 3 and for n 2 2, an = 2am-+1, express an in terms of n. 3. Let, a1 =3, a2 = 4 and for n…

A: Note:-Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: d) 85% of all students finish the activity in less than secon Submit Question

A: X~N( μ = 38.6 , ? = 6.3 ) μ = 38.6 , ? = 6.3 Z-score =( x - μ )/?

Q: Let, a, = 3, a2 = 4 and for n2 3, a,= 2an-1+ an-2 + n + 1, express a, in terms of n. %3D %3D %3D

A: The nth term of A.P is given by an=a+n-1d we have,  a=3,d=4-3=1an=3+n-11=2+n we get,…

Q: " Show that the integers m = 3* . 568 and n = 3k. 638, where k > 0, satisfy simultaneously t(m) =…

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Q: 1- Suppose A=

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Q: Let, a1 = 3 and for n > 2, an = 2an-1+ 1, express an in terms of n.

A: a1 = 3 and, an = 2an-1 + 1 for, n≥2 We have to find the generalized term using the recursion…

Q: Let, a, = 3, a2= 4 and for n2 3, a,= 2an-1+ an-2, express a, in terms of n. %3D

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: to: explicitly state the te- Σ2/ n=1

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Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 – 5, express an in terms of n.

A:

Q: 1. Let, a1 = 7 and for n > 2, an = "1 express an in terms of n.

A: According to our guidelines, we can solve only the first question. Please repost other questions as…

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + n², express an in terms of n.

A: In this question, we solve the recurrence relation  in terms of n an=2an-1+an-2+n2witha1=3a2=4

Q: et, a1 = 3, a2 = 4 and for n > 3,an = 2an-1 + an-2 +n², express an in terms of n. %3D

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Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

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Q: Find the generalized union and intersection: 3) A = {1,2,3,...} A₂ = {x|x = 22m where m eset of…

A: Given that, Λ={1,2,3,…} Λλ=x|x=2λm where m∈set of integers from -λ to +λ The objective is to find…

Q: Prove by Contradiction: There are no integers x and y such that = 4y+2.

A: We have to prove the statement "There are no integers x and y such that x2=4y+2" by contradiction.…

Q: 1. Let, a1 = 7 and for n > 2, an = " express a, in terms of n.

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Q: To show that r - 1= In(r-r+ 1) has at least two different positive root in R. 6.

A: We need to analyze the roots of the equation x-1=lnx2-x+1. This equation can be re-written as…

Q: of t/4 for x. (If an answer is undefined, enter UNDEFINED.)

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Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: 4. Let, a = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2 +n, express a, in terms of n.

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 +an-2 +n², express an in terms of n. %3D

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Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: Q2 1-The Euler's number (e) is a * rational number a. True b. False

A: Rational numbers are those which can be represented in the from of fraction and those which can not…

Q: B. Find a number that provides a counterexample to show that a given statement is false x, x³…

A: For all number x, (x+1)(x-1) over (x-1) is equals to x+1

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 +n², express an in terms of n.

A: a1=3, a2=4 n≥3; an=2an-1+an-2+n2 First from the given, the given values shows that the terms are in…

Q: - Show that (for n = 0, 1, 2, ..) (a) F(-n, b; c; 1) = - (c-b)n (c)n

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 2. Show that if a is an integer other than 0, then a) 1 divides a h) a divides 0

A:

Q: 4. Demonstrate that for positive integers t and Q, (t <= [V@]) is equivalent to (t x t <= Q). Show…

A: Given that t and Q are two positive integers and t≤Q To show that t×t≤Q Since from the given…

Q: n Show that (") = (,“,) n-r.

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Q: 2. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + 5n, express an in terms of n.

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Q: 11) Suppose an>0. Which of the followill

A: This is a question from the series.

Q: Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 +an-2 – 5, express an in terms of n.

A: We will first find the roots of characteristic equation and write general solution of homogeneous…

Q: suppose X=N(10, 1.924)Pr(X is less than or equal to 8.5)

A: Given a normal distribution with mean 10 and variance 1.924.the relationship between standard…

Q: 2. Let, a, = 3, a2 = 4 and for n 2 3, an= 2an-1+ an-2 + 5, express a, in terms of n.

A:

Q: Prove by contradiction that if a sum of three real numbers is less than 30, th at least one of the…

A: We have to prove by contradiction that if a sum of three real number is less than 30, then at least…

Q: Show that the integers m = 3k . 568 and n = 3k . 638, with k E Z>o, satisfy simultaneously $(m) =…

A:

Q: Express the following in closed form: (1+k)? k=1

A: The standard formula for the sum of integers is given by the expression ∑i=1ni=n(n+1)2. The standard…

Q: Enter a counterexample for the conclusion. If x is a prime number, then x+1 is not a prime number. A…

A: Prime numbers: The numbers which are divisible by 1 and by itself. The given conclusion is that if x…

Q: m above, prove that for every real number c>0, there is a 1/N < c.

A: In every real number c, there is integer N which is N &gt; c.