3. Evaluate |(n + 1)! – (n + 2)!|, where n E N.

Q: How many digits does a number 8^(n). 5^(3n+4)  have, if n belongs to N ?

A: Given data Number: 8n .5 (3n+4) We have to find digits in number.

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: Show that inf n e N} = 0. n1/3

A:

Q: . Show that n! > 3ª for n> 7.

A:

Q: C. n In n n=2

A:

Q: 00 In(n) . Σ n=2

A: According to question given that ∑n=2∞ln(n)n

Q: In(n + 3) n+3 n=2

A: By integral test we integrate the terms......

Q: Σ (-1) n=1 nyerges for all n20

A: Please refer to the image below

Q: In n 22. n=2 _n² 8

A: Given: ∑n=2∞ln(n)n2

Q: 5n. Determine for which n n-2 For nz 2, let on =

A: Here we have to determine the n for which |an|<1 for all n≥2 where an=5nn2-2

Q: Show that for any n E N, 7(15".

A:

Q: 5) Find the total Ħ of díagonals for af )n=5 b)n=10

A:

Q: How did they got n(n+1)(2n+1) / 6

A:

Q: 2) (n² – n – 29) ÷ (n – 6) 4) (k² – 7k + 10) ÷ (k – 1) tv

A:

Q: For every n E N, 1+3+5+ ·.+ (2n – 1) = n² + 3.

A:

Q: 3(3 + 1) n = 3: Show that 1 + 2 + 3 =

A: To show that 1 + 2 + 3 + ...  + n = n(n + 1)2 is true for the given value of n.   Also, to show…

Q: a)What is N? lo) What is Sx?

A:

Q: * if the o is not known and (n< 30) can be used z O

A: Which one is the correct choice

Q: is equal to. k=1 n2 The sum O n+1 2n O n+1 O n? +1 2n2

A:

Q: 14. If n e Z, then 5n2 +3n + 7 is odd. (Try cases.)

A: By method of direct proof, prove the statement " If n∈ℤ, then 5n2+3n+7is odd"k∈ℤk∈ℤ as follows.

Q: S n +1] (d) In(6n) { n=2

A: According to guidelines we solve one question.thanku

Q: In? (n) +7+ + 2" lim n→∞ 2n + 5 +n121212 + 4n n2 (d) 4+ + In4(n) + 4" + (n + 4)!

A:

Q: Droof that n! %3D1 オ=O K!(n=k)!

A:

Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

A:

Q: 2. The number of ways of arrangingr objects from n objects in order is called the number of . of n…

A: Given: The number of ways of arranging r objects from n objects in order is called thenumber of…

Q: 2. Prove that n²(n + 1)? 13 + 23 +...+ n3 4. for n e N.

A:

Q: Let n e Z. n#-1,3,

A:

Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

A:

Q: 4 + In(n*) \ D) { { } [ Select ] 2 + In n 4 + In(n*) E) n + In n [ Select ] 2n? + 2n + 4 F) { (-1)".…

A:

Q: 3n n² + 7 ) n=1 ather means

A: Given   Root test

Q: 2. Prove that n²>2n for n >2

A: Note that, the given statement P(n): n2&gt;2n for n≥2 has little correction because if n=2  then…

Q: For n ≥ 2, let an=5n/n2-2 Determine for which n, |an|<1

A: Use the given inequality for an and find the quadratic equation for n and solve

Q: Show that n! > 3ª for n > 7.

A: The given inequality is, n!&gt;3n We need to prove that, the inequality is true for n≥7 Firstly,…

Q: " n2 f) 1 1 + n? n=1 n/In(n)

A: To determine the convergence of the below series. ∑n=1∞n21+n2  and  ∑n=2∞1nlnn

Q: 1. Show that b, = (n!)'/n > 20.

A: Consider n!1n=an1n.

Q: For n≥2, let an= 5n/n2-2. Determine for which n, |an|<1.

A: Use the inequality on and find the inequality for n

Q: Prove Γ (n) = (n-1)! where n ∈ ℕ

A: Concept: The proof for this gamma integral will be done using mathematical induction

Q: Encontrar el enésimo término de las sucesiones 1 2 3 4 4'9'16' 25 3n an 1 1 an (n + 1)! °n =+ (n +…

A: Consider the sequence  14,29,316,425,........

Q: n(n – 1) is O(n²). 2 Show that

A: f(n) is O(g(n)) if there exist positive constants c and k such that f(n)≤c g(n) whenever n&gt;k.…

Q: (c) Show that for 2" > 4n for n ≥ 5.

A:

Q: solve for t

A: Given equation: eln2t=12

Q: 3. Evaluate |(n + 1)! - (n + 2)!|, where n E N.

A:

Q: If n is 0 what is 8n

A:

Q: The number N of deer in a certain population t years after observation began is given by  N =…

A: Given: The number N of deer in a certain population t years is To find: The deer population after…

Q: Find σ(n) if n = 2^k-1 (2^k - 3) where 2^k - 3 is prime

A:

Q: Show that for all n € N, one has 1 2√n+1 <√n+1-√n<; 2√ñ

A:

Q: n2 n+1 by root test. n+2 n=1

A:

Q: ined by - N = 0 will be

A:

Q: Suppose n e z. If n² is odd, then n is odd.

A:

Q: b) Prove that 2 < (1+1/n)" < 3 for all n e N Your answer

A: Solution: Consider the given  2≤1+1nn≤3  for all n∈ℕ Let an = 1+1nn, ∀n∈ℕ Then we have to show that…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.