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1. E- i = (E-,D² = ("*+2)* %3D1 %3D1 n(n+1)(n+2)(n+3) 2. E, i(i + 1)(i + 2)

1. E- i = (E-,D² = ("*+2)* %3D1 %3D1 n(n+1)(n+2)(n+3) 2. E, i(i + 1)(i + 2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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solve the ff problems and pls show the solution

I. MATHEMATICAL INDUCTION. Prove the ff. Formulas, show your solution: 2 1. E = (20² = ("*2) n(n+1)(n+2)(n+3) (n(n+1) 2. E, i(i + 1)(i +2) = II. COMPLEXITY NOTATIONS. If function f(n) belongs to 0, 0, Q notations, indicate by labeling along the side as correct; otherwise, label it as wrong. 1. Show that 200 € O(1) and 200 E Q(1). 2. Show that 2n+5 € O(n?) 3. Show that 3 log n +log (log n) € O(log n). 4. Show that n2/2 – 3n € Q(n²). 5. Show that 2n² € Q (n²).
Transcribed Image Text:I. MATHEMATICAL INDUCTION. Prove the ff. Formulas, show your solution: 2 1. E = (20² = ("*2) n(n+1)(n+2)(n+3) (n(n+1) 2. E, i(i + 1)(i +2) = II. COMPLEXITY NOTATIONS. If function f(n) belongs to 0, 0, Q notations, indicate by labeling along the side as correct; otherwise, label it as wrong. 1. Show that 200 € O(1) and 200 E Q(1). 2. Show that 2n+5 € O(n?) 3. Show that 3 log n +log (log n) € O(log n). 4. Show that n2/2 – 3n € Q(n²). 5. Show that 2n² € Q (n²).
III. GROWTH OF FUNCTIONS. Arrange the following mathematical terms from lowest to highest order. Given: n3 n? n! 2n 7n - 2 log n n log n 10n n5 + log n n? + n log n Example: a <b<c<d< ... <x <y<z IV. SIMPLIFYING RECURRENCES. Simplify the following recurrence relations, show your solution: 1. T(n) = 2T() + vn 2. T(n) = T() + 1 3. T(п) — 2T (п - 2) + logn 4. T(п) %3 9т () 3 + C 10 =
Transcribed Image Text:III. GROWTH OF FUNCTIONS. Arrange the following mathematical terms from lowest to highest order. Given: n3 n? n! 2n 7n - 2 log n n log n 10n n5 + log n n? + n log n Example: a <b<c<d< ... <x <y<z IV. SIMPLIFYING RECURRENCES. Simplify the following recurrence relations, show your solution: 1. T(n) = 2T() + vn 2. T(n) = T() + 1 3. T(п) — 2T (п - 2) + logn 4. T(п) %3 9т () 3 + C 10 =
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