5. Find the closed form solutions of the following recurrence relations with given initial conditions. Use forward substitution or backward substitution as described in Example 10 in the text. (a) an = −an−1, a0 = 5 (b) an = an−1 + 3, a0 = 1 (c) an = an−1 − n, a0 = 4 (d) an = 2nan−1, a0 = 3 (e) an = −an−1 + n − 1, a0 = 7
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5. Find the closed form solutions of the following recurrence
relations with given initial conditions. Use...
7. Find the solution of each of these recurrence relations with the given initial conditions. Use...
7. Find the solution of each of these recurrence relations with the given initial conditions. Use appropriate summation formulas to simplify your answers. a) an = (n + 1)an-1, ao = 5 The solution is: b) an=2an-1-3, a, = 5 c) an = An-1 + n-3, ao = 7
- Find the closed formula for each recurrence relations (show a clear image pls) 1. an...
- Find the closed formula for each recurrence
relations (show a clear image pls)
1. an = 1.1an-1, do = 1 2. An = -an-1, 0o = 5 3. An = An-1 - 2, do = 4
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-...
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0 (a) Find the generating function for an and then solve for an b) What is the homogeneous recurrence relation that an satisfies? (c) Repeat (a) and (b) for bn 72.
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0...
) Solve the following recurrence relation with the given initial conditions: an=10an-1-21an-2 a0=-3 a1=5
) Solve the following recurrence relation with the given initial conditions: an=10an-1-21an-2 a0=-3 a1=5
Problem 2. Find the closed formula for each of the following recurrence relations. 1. an =...
Problem 2. Find the closed formula for each of the following recurrence relations. 1. an = 1.lan-1, do = 1 2. a, = -n-1, 0o = 5 3. an = An-1-2, do = 4 Problem 3. Computer each of the sums below 1. Ei=30i, di = (-2) 2. 1-20, ai = 12 3. Sila, a; = i +5 (hint: this is an arithmetic sequence) Problem 4. Show that r? + 4x + 17 is 0(2) Problem 5. Put the functions...
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a) (3 pts) Find recurrence relations for the coefficents, an (b) (4 pts) Use the recurrence relation to g...
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a) (3 pts) Find recurrence relations for the coefficents, an (b) (4 pts) Use the recurrence relation to give the first three, n-zero terms of the power series solution to the initial value problem: y'-2xy = z, y(0) = 2 (c) (1 pt) Identify the solution as a common function (in closed form).
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a)...
Find the solution to the following lhcc recurrence: an=3nan−1 for n2 with initial conditions a0=4
Find the solution to the following lhcc recurrence:an=3nan−1 for n2 with initial conditions a0=4.
Problem 3 (10 points) Suppose a sequence satisfies the below given recurrence relation and initial conditions....
Problem 3 (10 points) Suppose a sequence satisfies the below given recurrence relation and initial conditions. Find an explicit formula for the sequence a -6a--9a,-2 for all integers k2 2 ao = 1, a1 = 3
For these recurrence relations, solve for general equation using characteristics and particular. Use initial condition if...
For these recurrence relations, solve for general equation using
characteristics and particular. Use initial condition if given.
a. fn+1 = 1 Initial condition: fo = 2 b. fn+1 -fn-n=0 n-1 1+fi = fn+1 Initial conditions: fo = 1, f1 = 1, n > 1 i=0
Find a closed form of the recurrence given by an = -6+12-an-1; do = 2. Show...
Find a closed form of the recurrence given by an = -6+12-an-1; do = 2. Show work.
7. Find the solution of each of these recurrence relations with the given initial conditions. Use appropriate summation formulas to simplify your answers. a) an = (n + 1)an-1, ao = 5 The solution is: b) an=2an-1-3, a, = 5 c) an = An-1 + n-3, ao = 7
- Find the closed formula for each recurrence
relations (show a clear image pls)
1. an = 1.1an-1, do = 1 2. An = -an-1, 0o = 5 3. An = An-1 - 2, do = 4
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0 (a) Find the generating function for an and then solve for an b) What is the homogeneous recurrence relation that an satisfies? (c) Repeat (a) and (b) for bn 72.
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0...
Problem 2. Find the closed formula for each of the following recurrence relations. 1. an = 1.lan-1, do = 1 2. a, = -n-1, 0o = 5 3. an = An-1-2, do = 4 Problem 3. Computer each of the sums below 1. Ei=30i, di = (-2) 2. 1-20, ai = 12 3. Sila, a; = i +5 (hint: this is an arithmetic sequence) Problem 4. Show that r? + 4x + 17 is 0(2) Problem 5. Put the functions...
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a) (3 pts) Find recurrence relations for the coefficents, an (b) (4 pts) Use the recurrence relation to give the first three, n-zero terms of the power series solution to the initial value problem: y'-2xy = z, y(0) = 2 (c) (1 pt) Identify the solution as a common function (in closed form).
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a)...
Problem 3 (10 points) Suppose a sequence satisfies the below given recurrence relation and initial conditions. Find an explicit formula for the sequence a -6a--9a,-2 for all integers k2 2 ao = 1, a1 = 3
For these recurrence relations, solve for general equation using
characteristics and particular. Use initial condition if given.
a. fn+1 = 1 Initial condition: fo = 2 b. fn+1 -fn-n=0 n-1 1+fi = fn+1 Initial conditions: fo = 1, f1 = 1, n > 1 i=0
Find a closed form of the recurrence given by an = -6+12-an-1; do = 2. Show work.
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