n n→ ∞ b. n Give an example of a pair of series Σ a, and Σ b, with positive terms where lim n=1 n=1 (anb) = Σ a converges. Σb diverges, but = 0 and Σ bn n=1 n=1

Binomial seriesa. Find the first four nonzero terms of the binomial series centered at 0 for the given function.b. Use the first four terms of the series to approximate the given quantity.

Find the sum of the convergent series. Σ 16 n(n + 2) n= 1

An individual is given a dose of Q units of a certain drug. the amount that remains in the bloodstream at the end of t minutes and Qe−ct, with c > 0. Suppose that the same dose is administered at successive intervals of T minutes. (a) Using series, express the amount A(k) of the drug in the bloodstream immediately after the K-th dose.(b) Find an upper bound for the amount of drug in the bloodstream after an arbitrary number of doses.(c) Find the shortest time between doses that ensures that A(k) does not exceed a certain level M, M > Q.

Question 2c

Find the sum of the convergent series. 8 Σ (4) η = 0

1+3* 4. Does the series converge? If so, find the sum. If not, explain why. 5k k=1 IM:

Determine which (if any) of the following series are conditionally convergent. Α. Σ(-1)" sin (n) B. (-1 c. E(-1)"+1 1 Inn п- Inn (-2)*+1 D. n+ 9" E.(-1)"; Inn F.E(-1)"+1, n3 +4 Note: there may be more than one correct answer. Select all that apply

Consider the function 1 1- x4 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were E, 3"x2n, you would write 1 + 3x? + 3?x* + 33x° + 34x$. Also indicate the radius of convergence. Partial Sum: Radius of Convergence: ..