(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

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milcah answered 2 years ago

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+⋯=

When does a series converge? Does the harmonic series converge? Can you find another series which...

When does a series converge? Does the harmonic series converge? Can you find another series which seems like it should converge , but it diverges? Does the alternating harmonic series converge?

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

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...

1. Find all the values of x such that the given series would converge. ∞∑n=1 (3x)^n/n^11...

1. Find all the values of x such that the given series would converge. ∞∑n=1 (3x)^n/n^11 The series is convergent from x = , left end included (enter Y or N): to x = , right end included (enter Y or N): 2. Find all the values of x such that the given series would converge. ∞∑n=1 5^n(x^n)(n+1) /(n+7) The series is convergent from x= , left end included (enter Y or N): to x= , right end included (enter Y or...

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b) Find the joint cumulative density function of (X,Y) c) Find the marginal pdf of X and Y. d) Find Pr[Y<X2] and Pr[X+Y>0.5]

Determine if the following series converge or diverge. If it converges, find the sum. a. ∑n=(3^n+1)/(2n)...

Determine if the following series converge or diverge. If it converges, find the sum. a. ∑n=(3^n+1)/(2n) (upper limit of sigma∞, lower limit is n=0) b.∑n=(cosnπ)/(2) (upper limit of sigma∞ , lower limit is n= 1 c.∑n=(40n)/(2n−1)^2(2n+1)^2 (upper limit of sigma ∞ lower limit is n= 1 d.)∑n = 2/(10)^n (upper limit of sigma ∞ , lower limit of sigma n= 10)

1. If f(x) = ln(x/4) -(a) Compute Taylor series for f at c = 4 -(b)...

1. If f(x) = ln(x/4) -(a) Compute Taylor series for f at c = 4 -(b) Use Taylor series truncated after n-th term to compute f(8/3) for n = 1,.....5 -(c) Compare the values from above with the values of f(8/3) and plot the errors as a function of n -(d) Show that Taylor series for f(x) = ln(x/4) at c = 4 represents the function f for x element [4,5]

A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where...

A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where A is an constant. Then compute the value of p(1<=X<=3) The answer will be either: 2/3, 3/4, 5/6, or 15/16 A discrete random variable X is uniformly distributed among −1,0,...,12. Then, what is its PMF for k=−1,0,...,12 The answer will be either: p(X = k) = 1/12, 1/13, 1/14, or 1

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

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