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(d) 1 + 2*+...+n° = n(n+1)(2n+1) (3n² +3n=1) for a 0, a # 1 %3D 30 a"-1 (e) 1+a+a? +...+ a"-1 a-1 (f) 32n + 7 is divisible by 8

(d) 1 + 2*+...+n° = n(n+1)(2n+1) (3n² +3n=1) for a 0, a # 1 %3D 30 a"-1 (e) 1+a+a? +...+ a"-1 a-1 (f) 32n + 7 is divisible by 8

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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Discrete Math. Please computerized and in image. Answer the d-f
2. Use mathematical induction to prove that the statements are true for every positive integer n. (a) 1+3 + 6 + ...+ n (n+1) n (n+1)(n+2) 5n (n+1) (b) 5 + 10 + 15 + ..+ 5n (c) 1² + 2³+ ...+n³ = n?(n+1)² %3D 4 (d) 1* + 2*+...+nª = n(n+1)(2n+1) (3n² +3n=1) %3D 30 a"- (e) 1+ a + a² +...+ a"-1 = for a + 0, a # 1 a-1 (f) 32n + 7 is divisible by 8 (g) 13" + 6" is divisible by 7 (h) 25n+1 + 52n+2 is divisible by 27 (i) 72n + 16n - 1 is divisible by 64 G) n3 –n is divisible by 3
Transcribed Image Text:2. Use mathematical induction to prove that the statements are true for every positive integer n. (a) 1+3 + 6 + ...+ n (n+1) n (n+1)(n+2) 5n (n+1) (b) 5 + 10 + 15 + ..+ 5n (c) 1² + 2³+ ...+n³ = n?(n+1)² %3D 4 (d) 1* + 2*+...+nª = n(n+1)(2n+1) (3n² +3n=1) %3D 30 a"- (e) 1+ a + a² +...+ a"-1 = for a + 0, a # 1 a-1 (f) 32n + 7 is divisible by 8 (g) 13" + 6" is divisible by 7 (h) 25n+1 + 52n+2 is divisible by 27 (i) 72n + 16n - 1 is divisible by 64 G) n3 –n is divisible by 3
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