Find L{(3t"+1 – 2)´}. - 2)') O 9(2n+1)! 4一3 g2n+2 O 9(2n+2)! 12(n+1)! 82n+3 sN+2 O 9(2n+2)! 2n+3 O 9(2!)(n+1)! 12(n+1)! s2n+3 sn+2 4一5

Q: 1. Prove that (1) (2) (3) + (2) (3) (4)+...+ n(n+1)(n+2) = "(n+1Xn+2}(n+3)

A: Given: - The statement is, (1)(2)(3)+(2)(3)(4)+......+n(n+1)(n+2)=n(n+1)(n+2)(n+3)4 To prove: - The…

Q: In Exercises 11–18, verify that the infinite series diverges.

A: " Since you have a asked multiple question, we will solve the first question for you. If you want…

Q: Given: In(1+ x) (-1)" xn+1 _if |x| < 1 n + 1 n=0 (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of…

A: Solving

Q: ind witnesses to show that n^3 − 5n^2 − 4n is O(n^3).

A: In this question, order of polynomial can be found with the help of Big-O notation. Big-O Notation…

Q: 1. Complexity 2n – n³ + 2 Prove that O(n) 3n2 + 4n – 1

A: The big O notation is used to mention the important term r the biggest term in the equation. The…

Q: In(1/n) an %3D V2n

A: Given: an=ln1n2n

Q: (c) Prove that 0 · Pn(0) +1· Pn(1) +2• Pn(2) +3· Pn(3)+...+n· Pn(n) = n! for all positive integers…

A: Let us consider all n! permutations of the set {1,2,3,..,n}. Given, pnk be the number of…

Q: Assume that S = Σ(-1)"-¹. 999 9 99 8 O 1000 10 1 (n + 1)5 n=1 n=1 Find the smallest integer N such…

A:

Q: Prove that 1-21 +2-22 + ……+n· 2" = (n – 1)2"+1+2 for any n E N. -

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

Q: Prove that πd/n n = nτ(n)/2.

A: your question has a silly mistake, it should be πd|n d = nτ(n)/2. supposeτ(n)=r , where r be the…

Q: Prove (m – n)² = m² – 2mn + n² . 1.

A:

Q: 4. With the fact of 1² +2²+...+ n² = n(n+1)(2n + 1)/6, prove that n n n(n −1) ΣΣ(i-j)² 6 i=1 j=1…

A:

Q: Given: In(1+x) = >) (-1)". -xn+1 if |x| < 1. n+1 n=0 Compute the exact value of -1)"(n+2) 2n+1(n +…

A: Given: ln(1+x)=∑n=0∞(-1)nn+1xn+1 where x&lt;1To Compute: Exact value of ∑n=0∞(-1)n(n+2)2n+1(n+1)

Q: - Prove that for all n E Z, we have ged(27n – 20, 4n – 3) = 1.

A: Solution

Q: The number of the element(s) of order 2 in Z3 O Z6 O 2 3

A: Given  ℤ3⊕ℤ6

Q: b) Prove that all numbers n > 20 can be represented as n = 4 * i +7*j for some non- negative i and j…

A: Prove that all numbers n≥ 20 can be represented as n = 4*i+7*j for some non- negative i and j by…

Q: Problem 5.3 Prove that n(n+1)(2n + 1) (3n² + 3n – 1) 30 j=1 whenever n is a positive integer.

A:

Q: -xx-9 and y=-x+3 у -9-8-7-6-5-4-3 1 y=x: POINT(S): IN 76 NWA -2 N3456789 -2 -3 -6 -7 -8 23456 -9 +2…

A: We have to find the graph

Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A:

Q: For neN, is f (n) = 3.2" - 3 a solution to the recurrence relation An = 3an-1-2an-2?

A: For the recurrence relation an = 3an - 1 - 2an - 2  we have f(n) = 3•2n - 3 for all n in N as a…

Q: 1. Prove that 12 + 22 + ...+ n² : n(n + 1)(2n + 1) %3D 6. for n e N.

A:

Q: Prove that n2+ 4n + 6 E O(n²)

A: Solution: The objective is to prove that the given statement

Q: 7. For every integer n z 1, n(5n – 3) 1+6+11+16++(5n– 4) 2

A: Solution is in step 2

Q: (-1)"(n+ 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A: Given series is  ∑n=0∞-1nn+22n+1n+1

Q: Problem 5.8 Prove, for all positive integers n, 1 3 2n – 1 1 < V3n 2 4 2n

A:

Q: *3. Prove that l' + 2 + .. +n =n(n+ 1(2n + 1) for all ne N.

A: By using induction.

Q: 18. Prove: n ΣΚ k = 0 = n(n + 1)(2n + 1) 6

A: The given problem is to prove the given following identity that sum of squares of first n natural…

Q: 8d:  use the binomial theorem to obtain the following series expansions

A: Using the binomial theorem for the series expansion, here is the general binomial form for the…

Q: 1. Prove that (fn+1fn+3 – fnfn+4)* = 4 for each positive integer n.

A: We need to prove this, fn+1fn+3-fnfn+42=4

Q: I. Prove the following by Mathematical Induction 1. 12 + 32 + 52 + ... + (2N - 1)2 =…

A:

Q: 5. Prove that for all n n [j³ = j=1 n² (n + 1)² 4

A:

Q: Show that 5n + 3 and 7n + 4 are relatively prime for all n.

A:

Q: Show that φ(n2) = nφ(n) for every n ∈ Z+.

A:

Q: 1. Prove that {2" : n E Z} = {,n :n E Z}.

A:

Q: 1 (b) Prove by induction that (3i – 2)² = ;n(6n² – 3n – 1) for n 2 1

A: We have to prove ∑i=1n3i-22=12n6n2-3n-1 for n≥1 by using mathematical induction.

Q: –1)" Given: In(1 + x) = > . if a < 1. n + 1 n=0 (-1)" (n +2) 2n+1(n +1) 4. Compute the exact value…

A:

Q: Show that Σ dn o(n) n for every positive integer n.

A:

Q: Prove that: "C. = 2" {1.3.5...(2n - 1)} n!

A: The left-hand side of the expression is: lhs=Cn2n=(2n)!n!(2n-n)!                               Use…

Q: Let n € Z. Prove that if 3 /n, then 3 | (2n² + 1).

A:

Q: Let a1 = a2 = 1 and suppose an = an-1 + an-2 for n ≥ 3. Prove that a1a2 + a2a3 + · · · + a2n-1a2n =…

A: We have given that , a1 = a2 = 1 Also , an = an-1 + an-2 We need to prove that ,  a1a2 + a2a3 +…

Q: 2. Show that for every n 2 2 and every 0 <k<n- 2, within the triangle of Binomial Coefficients k+2…

A: We will use properties of binomial coefficient  nCr  +  nCr-1=n+1Cr+1Note : nCr=nr=n!r! n-r!   Proof…

Q: For nɛN, is f(n) = 2"+1 – -la solution to the recurrence relation an = 2" + an-1?

A: Given that For n∈ℕ, f(n)=2n+1-1 is a solution to the recurrence relation an=2n+an-1.

Q: 11. If n is an odd integer, show that n + 4n² + 11 is of the form 16k.

A: If n is an an odd integer then we have to show that n4 + 4n2 + 11 is of the form 16k for some…

Q: Show that 6n – 1 and 12n+1 are relatively prime for any n e Z.

A:

Q: To prove 3+7+11+...+(4n − 1) = n(2n + 1) holds for an arbitrary n € Z+, in the inductive step, under…

A:

Q: Find L {(2 t" – 3) (t + 2)} 2(2n)! s2n+1 sn+1 O 2 (2n)! $2n+1 n! sn+1 4 n! 82n+1 n! n+1 8. O 2(n²!)…

A:

Q: -1)" =£ Given: In(1 + x) if x < 1. n + 1 n=0 (-1)" (n +2 2n+1(n + 1) 4. Compute the exact value of…

A: ln(1+x)=∑n=0∞(-1)nn+1xn+1     if x&lt;111-x=∑n=0∞xn  if x&lt;1

Q: QUESTION 3 Prove that 2n > n2 if n is an integer greater than 4. For the toolhar press AIT. E10 /RCL

A:

Q: = ( 4+x)-³. 00 n=0 00 00 118 00 (-1)^(n+1) (n + 2)x" in +3 2.4" (-1)^(n+4)! 2n! (-1)" (n+1) (n + 2)…

A: