Consider the series X∞ k=3 √ k/ (k − 1)^3/2 . (a) Determine whether or not...

Consider the series X∞ k=3 √ k/ (k − 1)^3/2 . (a) Determine whether or not the series converges or diverges. Show all your work! (b) Essay part. Which tests can be applied to determine the convergence or divergence of the above series. For each test explain in your own words why and how it can be applied, or why it cannot be applied. (i) (2 points) Divergence Test (ii) Limit Comparison test to X∞ k=2 1/k . (iii) Direct Comparison test to X∞ k=2 1 /k .

Expert Solution

milcah answered 2 years ago

Consider the series X∞ k=2 2k/ (k − 1)! . (a) Determine whether or not the...

Consider the series X∞ k=2 2k/ (k − 1)! . (a) Determine whether or not the series converges or diverges. Show all your work! (b) Essay part. Which tests can be applied to determine the convergence or divergence of the above series. For each test explain in your own words why and how it can be applied, or why it cannot be applied. (i) Divergence Test (ii) Direct Comparison test to X∞ k=2 2k /(k − 1). (iii) Ratio Test

Use a for loop to determine the sum of the rst 10 terms in the series 5k3, k % 1, 2, 3, . . . , 10.

using power series of 1/(1-x), a) derive the power series for 1/(9+x^2) and determine the radius...

using power series of 1/(1-x), a) derive the power series for 1/(9+x^2) and determine the radius of convergence of this power series b) use the result from (a) to derive the power series for tan^-1(x) and state the radius of convergence of this power series

1. Given the series: ∞∑k=1 2/k(k+2) does this series converge or diverge? converges diverges If the...

1. Given the series: ∞∑k=1 2/k(k+2) does this series converge or diverge? converges diverges If the series converges, find the sum of the series: ∞∑k=1 2/k(k+2)= 2. Given the series: 1+1/4+1/16+1/64+⋯ does this series converge or diverge? diverges converges If the series converges, find the sum of the series: 1+1/4+1/16+1/64+⋯=

Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such...

Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such that u is an harmonic function. (b) Find the harmonic conjugate v of u. (c) Obtain the expression of f = u + iv in terms of z = x + iy

(a) Does the series X∞ k=1 (−1)^k+1 /k + √ k converge? (b) Essay part. Which...

(a) Does the series X∞ k=1 (−1)^k+1 /k + √ k converge? (b) Essay part. Which tests can be applied to determine the convergence or divergence of the above series. For each test explain in your own words why and how it can be applied, or why it cannot be applied. (i) (2 points) Alternating Series Test. (ii) Absolute Convergence Test

1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then determine interval of...

1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then determine interval of convergence. 2. Find the coeffiecient on x^4 in the Maclaurin Series representation of the function g(x) = 1/ (1-2x)^2

Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this...

Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this production function (b) Does this production function have an uneconomic region? If so, describe the region algebraically. (Hint: your answer will be an inequality like this: K<5L)

Determine whether it is linear or nonlinear system: 1. y(t) = 3 + x(2t) 2. y(t)...

Determine whether it is linear or nonlinear system: 1. y(t) = 3 + x(2t) 2. y(t) = x(4t) 3. y(t) = -4t[x(2t)] 4. y(t) = e^2[x(2t)] 5. y(t) = x^5(t) 6. y(t) = cost[x(2t)]

Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2....

Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2. (a) Randomly pick a sample of size 20 from this distribution, find the probability that there are 2 to 4 (inclusive) of these taking negative values. (b) Randomly pick an observation X from this distribution, find the probability that it is between 1.2 and 1.4, i.e., P (1.2 < X < 1.4). (c) Randomly pick a sample of size 40 from this distribution, and...

Question