6a. Show that 2/n = 1/3n + 5/3n and use this identity to obtain the unit...

6a. Show that 2/n = 1/3n + 5/3n and use this identity to obtain the unit fraction decompositions of 2/25 , 2/65 , and 2/85 as given in the 2/n table in the Rhind Mathematical Papyrus.

6b. Show that 2/mn = 1/ (m ((m+n)/ 2 )) + 1/ (n ((m+n)/ 2 )) and use this identity to obtain the unit fraction decompositions of 2/7 , 2/35 , and 2/91 as given in the 2/n table in the Rhind Mathematical Papyrus.

6c. Verify that 2/ n = 1/n + 1/2n + 1/3n + 1/6n and use this identity to obtain the unit fraction decompositions of 2/101 as given in the 2/n table in the Rhind Mathematical Papyrus.

Expert Solution

Colby Messinger answered 2 years ago

1- Show that (n^3+3n^2+3n+1) / (n+1) is O (n2 ). Use the definition and proof of...

1- Show that (n^3+3n^2+3n+1) / (n+1) is O (n2 ). Use the definition and proof of big-O notation. 2- Prove using the definition of Omega notation that either 8 n is Ω (5 n ) or not. please help be with both

Calculate the Big-O time complexity. Show work 1. n^2 + 3n + 2 2. (n^2 +...

Calculate the Big-O time complexity. Show work 1. n^2 + 3n + 2 2. (n^2 + n)(n ^2 + π/2 ) 3. 1 + 2 + 3 + · · · + n − 1 + n

Derive the Sackur-Tetrode equation starting from the multiplicity givenin Ch. 2: Ω =(1/N!)(V^{N}/h^{3N})(pi^{3N/2}/3N^{2}!)(2mU)^{3N/2} The Sackur-Tetrode equation...

Derive the Sackur-Tetrode equation starting from the multiplicity givenin Ch. 2: Ω =(1/N!)(V^{N}/h^{3N})(pi^{3N/2}/3N^{2}!)(2mU)^{3N/2} The Sackur-Tetrode equation is: S=Nk[ln((V/N)((4pi*m*U)/(3Nh^{2}))^{3/2})+(5/2)]

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this...

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this is indeed the correct limit. (b) Use an epsilon, N argument to show that {1/(n^(1/2))} converges to 0. (c) Let k be a positive integer. Use an epsilon, N argument to show that {a/(n^(1/k))} converges to 0. (d) Show that if {Xn} converges to x, then the sequence {Xn^3} converges to x^3. This has to be an epsilon, N argument [Hint: Use the difference...

Find the value of ∑(−1)^n/(3n+1) from n=0 to ∞

If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))

Use generating functions to solve the following recurrence relation: an = 2an−1 + 3n , n...

Use generating functions to solve the following recurrence relation: an = 2an−1 + 3n , n ≥ 1 a0 = 2

Show that (1 + 2 +. . .+n)2 > 12 +. . .+ n2, for n...

Show that (1 + 2 +. . .+n)2 > 12 +. . .+ n2, for n ≥ 2.

Question 7 Use the definition of Ω to show that 20(?^3) + 5(n^2) ∈ Ω (?^3)...

Question 7 Use the definition of Ω to show that 20(?^3) + 5(n^2) ∈ Ω (?^3) Big-O, Omega, Theta complexity of functions, Running time equations of iterative functions & recursive functions, Substitution method & Master theorem Please answer within these topics.

1. a) Prove that if n is an odd number then 3n + 1is an even...

1. a) Prove that if n is an odd number then 3n + 1is an even number. Use direct proof. b) Prove that if n is an odd number then n^2+ 3 is divisible by 4. Use direct proof. 2. a) Prove that sum of an even number and an odd number is an odd number. Use direct proof. b) Prove that product of two rational numbers is a rational number. Use direct proof. 3. a) Prove that if n2is...

Question