Sequence and Series Homework Help

(3) Determine all values of p and q for which the following series converges: \sum_{k=2}^{\infty} \frac{1}{k^{a}(\ln k)^{p}}

Find the sum of the finite geometric series by using the formula for Sn.

Next question A radio commercial for a loan company states: "You only pay 34ę a day for each $500 borrowed." If you borrow $2,441 for 230 days, w 360-day year.)repay, and what annual interest rate is the company actually charging? (Ass

Find i (the rate per period) and n (the number of periods) for the following annuity.thle Monthly deposits of $305 are made for 8 years into an annuity that pays 7.5% compounded monthly....

8.(6 points) Use Maclaurin series and the Taylor's inequality to estimate the value of 4 cos 5° to four decimal-place accuracy.

E-Loan, an online lending service, recently offered 60-month auto loans at 5.4% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $371, how much can you borrow from E-Loan? What is the total interest you will pay for this loan?—

Find the sum of the solutions to the equation given. 2\left(9^{x}\right)-3^{x+2}+54=4\left(3^{x+1}\right) \text { (note, this is similar to problem } 8 \text { from the practice, so show all steps in order to get credit) }

Example 3: Use any test covered in 11.1-11.6 to determine whether the following seriesconverges ordiverges. \sum_{n=1}^{\infty} \frac{1-\sin n}{n^{3 / 2}}

1. (9 points) Determine whether the sequences listed below are increasing, decreasing,or not monotonic. \text { a. }\left\{\frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{n !}\right\} \text { b. }\left\{\frac{(-1)^{n} n^{3}}{2 n^{3}+2 n^{2}+1}\right\} \text { c. }\left\{n^{2} e^{-n}\right\}

1. Find explicit formulas for sequences of the form a₁, a2, a3, ... with the initial terms given below: 1/5, 3/20, 5/80, 7/320, 9/1280