3. (a) Rewrite the given expression as a sum whose generic term x . ∞∞
i. x ? nanxn−1 + ? akxk n=1 k=0
∞∞
? n−1 ? n
ii. nanx + x anx n=1 n=0
(b) Determine the an so that the equation
∞∞ ?nanxn−1 +2?anxn =0 n=1 n=0
is satisfied. Try to identify the function represented by the series
?∞ n n=0 anx .
use differential equations method
3. (a) Rewrite the given expression as a sum whose generic term x . ∞∞ i....
1) (a) Rewrite the expression k-0 as a sum whose generic term involves (b) Determine an so that the equation 0o k-0 is satisfied (c) If y(x) Σχ o anz", state the ODE which you solved in (b), and attempt to identify the function y(x) represented by the series.
Rewrite the given expression using a single power series whose general term involves x (x+1)(n-1" n-2 n-2 n-0 k-0 2c, +Co+[(k+1)kc,+(k+2)(k+1)c2 +c,] R-1 k+1+3)k +o} k-0 +1)eo1+( +2)( +1)2 +c]k k-0
Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series whose general term involves xk n = 2 n = 0 262 +6C4F*( (x + 2)(x + 1)(x+2+(x-2)(x) Need Help? Read It Talk to a Tutor
Q2-Σ Notation Review notation by investigating In this problem we will remind ourselves of 2k k O a) Consider the similar finite sum 2* k-0 Using n - 3, rewrite this expression in expanded form, and then evaluate it. b) Rewrite Expression (2) in expanded form for n-6, and then evaluate it c) Expression (2) becomes a better approximation to Expression (1) as n grows larger. To get an idea of what (1) is, evaluate (2) using n 100. Don't...
Exercise 2. 19 pts Manipulation of sums Rewrite the following series in only one sum whose generic term involves 2", i.e. in the form of Check your answer by writing down the first three nonzero terms! (a) (3 pts) (1-2) Ža(n = 1)emons (b) (3 pts) (c) (3 pts) +] (n = 1)ex**++
+ Rewrite the number 0.5 as the quotient of two integers. Find the sum of the given finite geometric series 0.5= (Type an integer or a simplified fraction.) The sum of the finite geometric series is Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 27+9+3+... Warren wanted to save money to purchase a new car. He started by saving $1 on the first of January. On the first of February, he saved $3....
Find the function represented by the power series. 00 X+Zn Σ n=0 X +3 X-3 x + 3 X-
+ 0/2 points Previous Answers ZillDiffEQ9 6.1.028. Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series whose general term involves x. k+2 k+1 2+2- k-10x Need Help? Read It Talk to a Tutor Submit Answer
i) Write a Sigma-notation summation for: the sum of the first “n” odd positive integers. For example, if n=4, it should sum like this: 1 + 3 + 5 + 7. ii) Starting with: 1+sum r^n, n=1 to infinity, rewrite it as just one summation without the 1+ out front. iii) Starting with: sum 1/n, n=1 to infinity, rewrite it as two terms out front, and then the sum starting at n=3. iv) Starting with: sum 1/(n+1), n=0 to 5,...
Problem 2: (a) Suppose you are given the differential equation Divide the equation be u and rescale time to show this can be written as Give the expression for t and λ in terms of t, wo and wi. (b) Assuming λ « 1, write the solution of the formiz(t)-Σοοολ"rn(t). Plugging this into equation (5), show you can write the equation as Σλ"(afr" + r"-Σ ntEn- r.r.)=0 46m-1 (c) Assume that each term in the sum over n must separately...