Homework Answers
Your question was little bit lengthier and you had no mentioned
any particular method to solve these, so i'm assuming that you know
a little bit of basic complex analysis...in part (d) i have
evaluated one sum and the other two are exactly same as this
one.further note that equation (alpha) which i mentioned at end is
the equation on 3rd image just above the crossed line where "now
consider is written.thank you.
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(b) Use the identities above and the formula for the sum of a geometric series to prove that if n...
1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identi...
Time series analysis
1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and j E 1,2,... ,n} then TL TL sin-(2Ttj/n)- n/2 so long as J关[m/2, where Laj is the greatest integer that is smaller than or equal to x (c) Show that when j 0 we have...
Prove the well-known formula for the sum of a geometric series. First show by cross-multiplying that...
Prove the well-known formula for the sum of a geometric series. First show by cross-multiplying that 1 + r + r2 + · · · + r^n = 1−r^(n+1)/1-r . Then assume that |r| < 1 and find the limit as n → ∞.
a) Using the geometric sum formula, prove the relation below: N oen = {o otherwise k...
a) Using the geometric sum formula, prove the relation below: N oen = {o otherwise k = 0, +N ,t2N, ....... nad b) For illustration, consider now the complex signals xk (n) = e' lkn with N=6. Illustrate the validity of the relation in part (a) by sketching six plots on the complex plane for every value k=0, 1,2,3,4,5 and n=0,1,2,3,4,5.
(1) Give a formula for SUM{i} [i changes from i=a to i=n], where a is an...
(1) Give a formula for SUM{i} [i changes from i=a to i=n], where a is an integer between 1 and n. (2) Suppose Algorithm-1 does f(n) = n**2 + 4n steps in the worst case, and Algorithm-2 does g(n) = 29n + 3 steps in the worst case, for inputs of size n. For what input sizes is Algorithm-1 faster than Algorithm-2 (in the worst case)? (3) Prove or disprove: SUM{i**2} [where i changes from i=1 to i=n] ϵ tetha(n**2)....
Problem 3. Some bond calculus. (Hint: for this exercise, the formula for a geometric series might...
Problem 3. Some bond calculus. (Hint: for this exercise, the formula for a geometric series might be useful: if q 1, then 1-q I will assume in the future, that this formula is well known. 1. Suppose a coupon bond has a face value F0 to be repaid after n years and promises to pay a coupon C equal to an interest rate of r percent of that face value for all years t = 1, . . . ,n...
A) 0.2028 B) 0.4055 C) 0.47 D) 0.235 For the series given, determine how large n must be so that ...
please
A) 0.2028 B) 0.4055 C) 0.47 D) 0.235 For the series given, determine how large n must be so that using the nth partial sum to approximate the series gives an error of no more than the stated error. 20) 20) A) 600 B) 1500 C) 300 D) 3000 Use the Comparison Test to determine if the series converges or diverges. an=_cosn -4 t cos n n-1 n A) diverges S>소 Converge 6)or verges 21) due-toe-sones, 21) n s...
Main topic and problems for the final project The main purpose of the project is to introduce you how to use a in a...
Main topic and problems for the final project The main purpose of the project is to introduce you how to use a in an computer as a research tool Introductory Discrete Mathematics. In this project you will be asked to show how the Fibonacci sequence {Fn} is related to Pascal's triangle using the following identities by hand for small and then by computers with large n. Finally, to rove the identity by mathematical arguments, such as inductions or combinatorics. I...
2 (1) For z E C, define exp z - n-0 (a) Prove that the infinite series converges absolutely for z E C (b) Prove that when z є R, the definition of exp z given above is consistent with the one given i...
2 (1) For z E C, define exp z - n-0 (a) Prove that the infinite series converges absolutely for z E C (b) Prove that when z є R, the definition of exp z given above is consistent with the one given in problem (2a), assignment 16. Definition from Problem (2a): L(x(1/t)dt E(z) = L-1 (z)
2 (1) For z E C, define exp z - n-0 (a) Prove that the infinite series converges absolutely for z E C...
Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor'...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a pow...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a power series for h(), and find the radius of convergence Ri for h'(x). Find the smallest reasonable positive integer n so that - (b) (10) Let A- differs from A by less than 0.01. Give reasons. 5. (a) (10) Let g(x) sin z. Write down the Taylor series for...
Time series analysis
1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and j E 1,2,... ,n} then TL TL sin-(2Ttj/n)- n/2 so long as J关[m/2, where Laj is the greatest integer that is smaller than or equal to x (c) Show that when j 0 we have...
a) Using the geometric sum formula, prove the relation below: N oen = {o otherwise k = 0, +N ,t2N, ....... nad b) For illustration, consider now the complex signals xk (n) = e' lkn with N=6. Illustrate the validity of the relation in part (a) by sketching six plots on the complex plane for every value k=0, 1,2,3,4,5 and n=0,1,2,3,4,5.
Problem 3. Some bond calculus. (Hint: for this exercise, the formula for a geometric series might be useful: if q 1, then 1-q I will assume in the future, that this formula is well known. 1. Suppose a coupon bond has a face value F0 to be repaid after n years and promises to pay a coupon C equal to an interest rate of r percent of that face value for all years t = 1, . . . ,n...
please
A) 0.2028 B) 0.4055 C) 0.47 D) 0.235 For the series given, determine how large n must be so that using the nth partial sum to approximate the series gives an error of no more than the stated error. 20) 20) A) 600 B) 1500 C) 300 D) 3000 Use the Comparison Test to determine if the series converges or diverges. an=_cosn -4 t cos n n-1 n A) diverges S>소 Converge 6)or verges 21) due-toe-sones, 21) n s...
Main topic and problems for the final project The main purpose of the project is to introduce you how to use a in an computer as a research tool Introductory Discrete Mathematics. In this project you will be asked to show how the Fibonacci sequence {Fn} is related to Pascal's triangle using the following identities by hand for small and then by computers with large n. Finally, to rove the identity by mathematical arguments, such as inductions or combinatorics. I...
2 (1) For z E C, define exp z - n-0 (a) Prove that the infinite series converges absolutely for z E C (b) Prove that when z є R, the definition of exp z given above is consistent with the one given in problem (2a), assignment 16. Definition from Problem (2a): L(x(1/t)dt E(z) = L-1 (z)
2 (1) For z E C, define exp z - n-0 (a) Prove that the infinite series converges absolutely for z E C...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a power series for h(), and find the radius of convergence Ri for h'(x). Find the smallest reasonable positive integer n so that - (b) (10) Let A- differs from A by less than 0.01. Give reasons. 5. (a) (10) Let g(x) sin z. Write down the Taylor series for...
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