For each of the following, find both a closed form representation that just depends on n,...
For each of the following, find both a closed form representation that just depends on n, like 1(a) and a recursive representation (ie. a way to define each term based on previous term/terms and knowing how it begins, like 1(b)
a. 2, 6, 10, 14....
b. 9, 3, 1, 1/3, 1/9, 1/27...
c. 1, -1, 1, -1, 1, -1.....
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For each of the following, find both a closed form
representation that just depends on n,...
Find the closed form for each T(n given as a recurrence: 4 | T(m - 1)...
Find the closed form for each T(n given as a recurrence: 4 | T(m - 1) + 2 : n > 2 2 T(n) = T(n-1) + 4n -3 : : n=1 n> 1 1 2 n= 1 | 2T(n − 1)-1 : n> 2 T(m) = { 27 (m-1)+m-, : m=1 T(m) = 21 m - 1) + m : . m m -1 =1 > 1 5. Let n = 2m - 1. Rewrite your answer of the...
Find a closed form for sn=∑i=1n(5i−1). What is the first term of this sum? What is the nth term of the sum? If we write...
Find a closed form for sn=∑i=1n(5i−1). What is the first term of this sum? What is the nth term of the sum? If we write the sum both forwards and backwards and pair the terms vertically, what is the identical sum for each pair? Finally, give the closed form for sn=∑i=1n(5i−1). Find a closed form for sn=∑i=1n(8i−9). sn= Find a closed form for sn=∑i=1n(17−9i). sn= Find a closed form for sn=∑i=1n(−4−3i). sn=
For each transformation below, find the closed form of the transformation. 1) Let T be a...
For each transformation below, find the closed form of the transformation. 1) Let T be a linear transformation from R$ to M22 (R) [i Let B=1 0:00 [. :] [11] [12] [0 ] Let C= 12 41 -17 -5 65 -27 92 Let M = be the matrix transformation of T from basis B to C 17 58 -15 -51 81 The closed form of the transformation is Tb 3-1 2) Let T be a linear transformation from P3(R) to...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T la +(-1) 6+2c +(-1)d - 1a + 2b + 0c + Od -3a + 56+ (-1) +0d 2a +(-2) b + 3c +0d] с d T-1 2) Let T(a + bx + cx+ dx?) = 1a + 2b + 1c +(-1)d la + 3b + 3c + Od 3a + 7b +6c+(-3) d 8a + 196 +16c+(-6) d 1-[]- 3) Let T 13a +(-17)...
Problem 3 (a) Determine the Fourier series representation of the function By integrating each ter...
Problem 3 (a) Determine the Fourier series representation of the function By integrating each term of the series from 0 to x, find the Fourier series of function and use your result to deduce the exact value of the series (b) The Kronecker delta function, which depends on two variables m and n, is defined as 1 ifm=n The Kronecker delta function appears frequently in quantum mechanics, particularly in the plane waves basis description of single electron quantum states. Suppose...
1. The following is the extensive-form representation (omitting payoffs) of a game: ·N = {1, 2,...
1. The following is the extensive-form representation (omitting payoffs) of a game: ·N = {1, 2, 3): . H = 10, A, B, C. Ay, An, Ayy, Ayr, Any, Ann. Ba, Bb. Bc,CY.CN,CYY, CYN,CNY, CNN): ·Z = {Ayy, Ayn, Any, Ann, Ba, Bb. Bc, CYy, CYN,CNY, CNN): (1) Draw the corresponding game tree of the game; (8 points) (2) Write down the sets of strategies for each player; (7 points) (3) Suppose the information sets in this game are: (0),...
5. Find the closed form solutions of the following recurrence relations with given initial conditions. Use...
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
5. Find the closed form solutions of the...
3. Find a closed form for the generating function for each of these sequences (a) 7,3,4,6,7,3,4, 6,7,3,4,6,(b) 1,0.01,0.001,0.0001,... (c) 2,5,8, 11, 14, 17, 20, (e) 11,101, 1001, 10001, 100001, (d)...
3. Find a closed form for the generating function for each of these sequences (a) 7,3,4,6,7,3,4, 6,7,3,4,6,(b) 1,0.01,0.001,0.0001,... (c) 2,5,8, 11, 14, 17, 20, (e) 11,101, 1001, 10001, 100001, (d) 1×2×3, 2 x 3 x 4, 3 x 4 x 5, 4 × 5 × 6, ..
3. Find a closed form for the generating function for each of these sequences (a) 7,3,4,6,7,3,4, 6,7,3,4,6,(b) 1,0.01,0.001,0.0001,... (c) 2,5,8, 11, 14, 17, 20, (e) 11,101, 1001, 10001, 100001, (d) 1×2×3, 2 x...
7. Find the next two terms of each geometric sequence. a.-3.9. - 27. 81.... b. I....
7. Find the next two terms of each geometric sequence. a.-3.9. - 27. 81.... b. I. -1.1.-1.1. - 1.... 8. Find the first five terms of the geometric sequence for which ,- -2 and 3. 9. Find , for the geometric sequence 60, 30, 15.... 10. Write an equation for the nth term of the geometric sequence 4, 8, 16,... 11. The second term in a geometric sequence is -2 and the third term is-6. Find an equation for the...
1.we need n-1 comparisons at most 3*n/2comparisons suffice to find both the min and max Basic...
1.we need n-1 comparisons at most 3*n/2comparisons suffice to find both the min and max Basic Strategy: Maintain the minimum and maximum of elements seen so far. Don't compare each element to the minimum and maximum separately. Process elements in pairs. Compare the elements of a pair to each other. Then compare the larger element to the maximum so far, and compare the smaller element to the minimum so far. This leads to only 3 comparisons for every 2 elements...
Find the closed form for each T(n given as a recurrence: 4 | T(m - 1) + 2 : n > 2 2 T(n) = T(n-1) + 4n -3 : : n=1 n> 1 1 2 n= 1 | 2T(n − 1)-1 : n> 2 T(m) = { 27 (m-1)+m-, : m=1 T(m) = 21 m - 1) + m : . m m -1 =1 > 1 5. Let n = 2m - 1. Rewrite your answer of the...
For each transformation below, find the closed form of the transformation. 1) Let T be a linear transformation from R$ to M22 (R) [i Let B=1 0:00 [. :] [11] [12] [0 ] Let C= 12 41 -17 -5 65 -27 92 Let M = be the matrix transformation of T from basis B to C 17 58 -15 -51 81 The closed form of the transformation is Tb 3-1 2) Let T be a linear transformation from P3(R) to...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T la +(-1) 6+2c +(-1)d - 1a + 2b + 0c + Od -3a + 56+ (-1) +0d 2a +(-2) b + 3c +0d] с d T-1 2) Let T(a + bx + cx+ dx?) = 1a + 2b + 1c +(-1)d la + 3b + 3c + Od 3a + 7b +6c+(-3) d 8a + 196 +16c+(-6) d 1-[]- 3) Let T 13a +(-17)...
Problem 3 (a) Determine the Fourier series representation of the function By integrating each term of the series from 0 to x, find the Fourier series of function and use your result to deduce the exact value of the series (b) The Kronecker delta function, which depends on two variables m and n, is defined as 1 ifm=n The Kronecker delta function appears frequently in quantum mechanics, particularly in the plane waves basis description of single electron quantum states. Suppose...
1. The following is the extensive-form representation (omitting payoffs) of a game: ·N = {1, 2, 3): . H = 10, A, B, C. Ay, An, Ayy, Ayr, Any, Ann. Ba, Bb. Bc,CY.CN,CYY, CYN,CNY, CNN): ·Z = {Ayy, Ayn, Any, Ann, Ba, Bb. Bc, CYy, CYN,CNY, CNN): (1) Draw the corresponding game tree of the game; (8 points) (2) Write down the sets of strategies for each player; (7 points) (3) Suppose the information sets in this game are: (0),...
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
5. Find the closed form solutions of the...
3. Find a closed form for the generating function for each of these sequences (a) 7,3,4,6,7,3,4, 6,7,3,4,6,(b) 1,0.01,0.001,0.0001,... (c) 2,5,8, 11, 14, 17, 20, (e) 11,101, 1001, 10001, 100001, (d) 1×2×3, 2 x 3 x 4, 3 x 4 x 5, 4 × 5 × 6, ..
3. Find a closed form for the generating function for each of these sequences (a) 7,3,4,6,7,3,4, 6,7,3,4,6,(b) 1,0.01,0.001,0.0001,... (c) 2,5,8, 11, 14, 17, 20, (e) 11,101, 1001, 10001, 100001, (d) 1×2×3, 2 x...
7. Find the next two terms of each geometric sequence. a.-3.9. - 27. 81.... b. I. -1.1.-1.1. - 1.... 8. Find the first five terms of the geometric sequence for which ,- -2 and 3. 9. Find , for the geometric sequence 60, 30, 15.... 10. Write an equation for the nth term of the geometric sequence 4, 8, 16,... 11. The second term in a geometric sequence is -2 and the third term is-6. Find an equation for the...
1.we need n-1 comparisons at most 3*n/2comparisons suffice to find both the min and max Basic Strategy: Maintain the minimum and maximum of elements seen so far. Don't compare each element to the minimum and maximum separately. Process elements in pairs. Compare the elements of a pair to each other. Then compare the larger element to the maximum so far, and compare the smaller element to the minimum so far. This leads to only 3 comparisons for every 2 elements...
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