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

Expert Solution

milcah answered 3 years ago

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...

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+⋯=

Is 2k-1 odd? I get that 2(some int k) + 1 is the property for odd...

Is 2k-1 odd? I get that 2(some int k) + 1 is the property for odd numbers. The main question: I am confused on how 2k-1= 2k-2+1 which is a form of k?

(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

1.Prove that{2k+1:k∈N}∩{2k2 :k∈N}=∅. 2.Give two examples of ordered sets where the meaning of ” ≤ ”...

1.Prove that{2k+1:k∈N}∩{2k2 :k∈N}=∅. 2.Give two examples of ordered sets where the meaning of ” ≤ ” is not the same as the one used with the set of real numbers R.

Let f(x)= kx^k-x^(k-1)-x^(k-2)-...-x-1, where k is an integer greater than or equal to 1. Prove the...

Let f(x)= kx^k-x^(k-1)-x^(k-2)-...-x-1, where k is an integer greater than or equal to 1. Prove the roots of f have absolute value less than or equal to 1. This is possibly using Cauchy's Estimates for Roots of Polynomials or Ostrowski's Theorem, but I'm not sure how to use them.

Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant....

Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant. This velocity potential is commonly used to describe flow impinging upon a plate. Derive an equation for dP/dy, the pressure gradient in the y-direction, if the fluid has density, rho.

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

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