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We expect the closed form solution have a polynomial function by n. The first step to find the closed form solution is to decide the degree of the polynomial function. According to the recursive solution, H(5) = H(4) + (d)]. Therefore, we can get the sequence of differences between each H(n) is 6. (a) 0 ,and (d) ,which are resulted from They can also make relations with differences in between as follows: 6+ (e) =|(a) |(a) + (e) = (b) |(b) +(e) (d) As you can see, they have a constant difference (e) degree of the closed form solution's function is 2 because the second sequence is a constant. Therefore, it suggests the sequence may have a formula of the form: ] regardless of n. We can guess the H, (n) = An² + Bn + C, where A, B, C are integer. To find out A, B, C, we need at least three equations as follows: H(1) = 1 = A(1)² + B(1) + C H(2) = 7 = A(2)² + B(2) + C H(3) = 19 = A(3)² + B(3) + C We can find A =|(f) B =(g) .C = [(h) therefore the closed form solution is: H,(n) = [(f) n² + (g) n +|(h) | II

We expect the closed form solution have a polynomial function by n. The first step to find the closed form solution is to decide the degree of the polynomial function. According to the recursive solution, H(5) = H(4) + (d)]. Therefore, we can get the sequence of differences between each H(n) is 6. (a) 0 ,and (d) ,which are resulted from They can also make relations with differences in between as follows: 6+ (e) =|(a) |(a) + (e) = (b) |(b) +(e) (d) As you can see, they have a constant difference (e) degree of the closed form solution's function is 2 because the second sequence is a constant. Therefore, it suggests the sequence may have a formula of the form: ] regardless of n. We can guess the H, (n) = An² + Bn + C, where A, B, C are integer. To find out A, B, C, we need at least three equations as follows: H(1) = 1 = A(1)² + B(1) + C H(2) = 7 = A(2)² + B(2) + C H(3) = 19 = A(3)² + B(3) + C We can find A =|(f) B =(g) .C = [(h) therefore the closed form solution is: H,(n) = [(f) n² + (g) n +|(h) | II

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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We expect the closed form solution have a polynomial function by n. The first step to find the closed form solution is to decide the degree of the polynomial function. According to the recursive solution, H(5) = H(4) + (d). Therefore, we can get the sequence of differences between each H(n) is 6, (a) (b) , and (d) which are resulted from (c) They can also make relations with differences in between as follows: 6 +(e) (a) (a) +(e) (b) (b) +|(e) = (d) As you can see, they have a constant difference (e) regardless of n. We can guess the degree of the closed form solution's function is 2 because the second sequence is a constant. Therefore, it suggests the sequence may have a formula of the form: H,(n) = An? + Bn + C, where A, B, C are integer. To find out A, B, C, we need at least three equations as follows: H(1) = 1 = A(1)² + B(1) + C H(2) = 7 = A(2)² + B(2) + C H(3) = 19 = A(3)² + B(3) + C We can find A =|(f) B =|(g) C = (h) therefore the closed form solution is: H;(n) = (f) n² + (g) n + (h) |
Transcribed Image Text:We expect the closed form solution have a polynomial function by n. The first step to find the closed form solution is to decide the degree of the polynomial function. According to the recursive solution, H(5) = H(4) + (d). Therefore, we can get the sequence of differences between each H(n) is 6, (a) (b) , and (d) which are resulted from (c) They can also make relations with differences in between as follows: 6 +(e) (a) (a) +(e) (b) (b) +|(e) = (d) As you can see, they have a constant difference (e) regardless of n. We can guess the degree of the closed form solution's function is 2 because the second sequence is a constant. Therefore, it suggests the sequence may have a formula of the form: H,(n) = An? + Bn + C, where A, B, C are integer. To find out A, B, C, we need at least three equations as follows: H(1) = 1 = A(1)² + B(1) + C H(2) = 7 = A(2)² + B(2) + C H(3) = 19 = A(3)² + B(3) + C We can find A =|(f) B =|(g) C = (h) therefore the closed form solution is: H;(n) = (f) n² + (g) n + (h) |
Let H(n) be the number of circles you need to form a hexagon with n circles on each edge. Here's examples when each edge has 1, 2, 3, and 4 circles. There are 1, 7, 19 and 37 circles respectively. Note that the circles on an each are blue. Н 1) — 1 H(2) = 7 Н(3) 3 19 Н(4) 3 37
Transcribed Image Text:Let H(n) be the number of circles you need to form a hexagon with n circles on each edge. Here's examples when each edge has 1, 2, 3, and 4 circles. There are 1, 7, 19 and 37 circles respectively. Note that the circles on an each are blue. Н 1) — 1 H(2) = 7 Н(3) 3 19 Н(4) 3 37
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