Define cauchy sequences, Math 104: Homework 3. Let (sn) and

Define cauchy sequences

Assignment Help Mathematics

Reference no: EM131081498

Math 104: Homework 3-

1. Let (a_n) be a sequence defined according to a₁ = t where t > 0, and a_n+1 = 2a_n/(1+a_n) for n ∈ N. Prove that a_n → 1 as n → ∞.

2. Let (s_n) and (t_n) be Cauchy sequences defined on R, and let (un) be a sequence defined as u_n = as_n + bt_n for all n, where a, b ∈ R. By using the definition of a Cauchy sequence only, without assuming that limits of (s_n) and (t_n) exist, prove that (u_n) is a Cauchy sequence.

3. Let (s_n) be a sequence defined by s_n = (-1)ⁿ(1 + 1/n). Prove that lim sup s_n = 1 and lim infs_n = -1.

Reference no: EM131081498

Questions Cloud

What is the company unlevered cost of equity capital : Twice Shy Industries has a debt−equity ratio of 1.4. Its WACC is 9.4 percent, and its cost of debt is 6.7 percent. The corporate tax rate is 35 percent. What is the company’s cost of equity capital? What is the company’s unlevered cost of equity capi..

Smallest expected loss in the coming year with probability : DW Co. stock has an annual return mean and standard deviation of 8 percent and 31 percent, respectively. What is the smallest expected loss in the coming year with a probability of 16 percent?

Forecast level would you be neutral to make-buy decision : You can buy product X from company ABC for $33/piece. Alternatively, you can make product X in-house. You would have to purchase a small building at $200,000, purchase two machines at $40,000 and $28,000, and hire two operators for the machines. At w..

What is the IRR for the incremental investment : What option should be chosen if MARR = 12%? What is the IRR for the incremental investment? Use your calculated IRR to justify whether or not your chosen option is still the correct one if the MARR is 21%

Define cauchy sequences : Math 104: Homework 3. Let (sn) and (tn) be Cauchy sequences defined on R, and let (un) be a sequence defined as un = asn + btn for all n, where a, b ∈ R. By using the definition of a Cauchy sequence only, without assuming that limits of (sn) and (tn)..

What exactly is the payback period for this investment : You plan to propose the purchase of a machine to the engineering manager and you expect her to ask for the payback period of this investment. You also know that she generally doesn’t approve anything with a payback of over five years. Should you go a..

What will the retained earnings account value be after spilt : Jean's Warehouse has 16,000 shares of stock outstanding. The current market value of the firm is $768,000. The company has retained earnings of $130,000, paid in surplus of $321,000, and a common stock account value of 16,000. The company is planning..

Contemplating replacing current fleet of delivery vehicles : Your company is contemplating replacing their current fleet of delivery vehicles with Nissan NV vans. You will be replacing 5 fully-depreciated vans, which you think you can sell for $3,000 apiece and which you could probably use for another 2 years ..

Concerns effect of taxes on the various break-even measures : This problem concerns the effect of taxes on the various break-even measures. Consider a project to supply Detroit with 25,000 tons of machine screws annually for automobile production. Calculate the accounting, cash, and financial break-even quantit..

User Account

All Pages