Question

Let pp be a polynomial, and let θ∈(−1,1)θ∈(−1,1). Show that the series ∑∞k=1p(k)θk∑k=1∞p(k)θk converges absolutely.

Let pp be a polynomial, and let θ∈(−1,1)θ∈(−1,1). Show that the series ∑∞k=1p(k)θk∑k=1∞p(k)θk converges absolutely.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Determine if the series, k = 1 to ∞ , with terms (-1)k ((k - 1)/(k3/2...
Determine if the series, k = 1 to ∞ , with terms (-1)k ((k - 1)/(k3/2 + 1))2 converges absolutely, converges conditionally, or diverges. Tell which convergence test you are using.
Let p(x) be an irreducible polynomial of degree n over a finite field K. Show that...
Let p(x) be an irreducible polynomial of degree n over a finite field K. Show that its Galois group over K is cyclic of order n and then show how the Galois group of x3 − 1 over Q is cyclic of order 2.
Determine if the series converges conditionally, converges absolutely, or diverges. /sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4) /sum(n=1 to...
Determine if the series converges conditionally, converges absolutely, or diverges. /sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4) /sum(n=1 to infinity) sin(4n)/4^n
Problem 1 Let X1, · · · , Xn IID∼ p(x; θ) = 1/2 (1 +θx),...
Problem 1 Let X1, · · · , Xn IID∼ p(x; θ) = 1/2 (1 +θx), −1 < x < 1, −1 < θ < 1. 1. Estimate θ using the method of moments. 2. Show that the above MoM is consistent by showing it’s mean square error converges to 0 as n goes to infinity. 3. Find its asymptotic distribution.
Show that the series sum(an) from n=1 to infinity where each an >= 0 converges if...
Show that the series sum(an) from n=1 to infinity where each an >= 0 converges if and only if for every epsilon>0 there is an integer N such that | sum(ak ) from k=N to infinity | < epsilon
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use the P-test. (You could...
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use the P-test. (You could also use the Integral Test, as is the case with all series of this type.) According to the P-test: ∞∑k=1 1/5√k^3 converges the P-test does not apply to ∞∑k=1 1/5√k^3 ∞∑k=1 1/5√k^3 diverges Now compute s4, the partial sum consisting of the first 4 terms of ∞∑k=1 1 /5√k^3: s4= 2. Test the series below for convergence using the Ratio Test. ∞∑n=1 n^5 /1.2^n...
Let z0 be a zero of the polynomial P(z)=a0 +a1z+a2z2 +···+anzn of degree n (n ≥...
Let z0 be a zero of the polynomial P(z)=a0 +a1z+a2z2 +···+anzn of degree n (n ≥ 1). Show in the following way that P(z) = (z − z0)Q(z) where Q(z) is a polynomial of degree n − 1. (an ̸=0) (k=2,3,...). (a) Verify that zk−zk=(z−z)(zk−1+zk−2z +···+zzk−2+zk−1) 00000 (b) Use the factorization in part (a) to show that P(z) − P(z0) = (z − z0)Q(z) where Q(z) is a polynomial of degree n − 1, and deduce the desired result from...
3. Let P = (a cos θ, b sin θ), where θ is not a multiple...
3. Let P = (a cos θ, b sin θ), where θ is not a multiple of π/2 be a point on the ellipse (x 2/ a2 )+ (y 2/ b 2) = 1, where a ≥ b > 0; and let P1 = (a cos θ, a sin θ) the corresponding on the circle x 2 /a2 + y 2/ a2 = 1. Prove that the tangent to the ellipse at P and the tangent to the circle at...
let x be a discrete random variable with positive integer outputs. show that P(x=k) = P(...
let x be a discrete random variable with positive integer outputs. show that P(x=k) = P( x> k-1)- P( X>k) for any positive integer k. assume that for all k>=1 we have P(x>k)=q^k. use (a) to show that x is a geometric random variable.
Let f = sin(yz) + ln(x) a) Find the derivative of F at P(1,1,Pi) in the...
Let f = sin(yz) + ln(x) a) Find the derivative of F at P(1,1,Pi) in the direction of v = i+j-k b) Find a vector u in the direction where f increases the fastest c) Find a nonzero vector w with the property that the derivative of f in the direction of w at P(1,1,pi) is 0
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT