2. For each of the following statements • Write down a roadmap for a proof of it by induction. • Fill in the details of your roadmap to prove the statement. (i) n! < n" for all n e N. 1 (ii) m3" > 100 × 2" for all n € N with n > 23. [You may use a calculator 100 for the base case. - 6ak Define the sequence (ak)kEN by a1 = 2, a2 = 5 and ak+2 = for all k > 1. Then an = 2"-1 +3"-1 for all n > 1. 11 5ak+1 %3D

Question
2. For each of the following statements
• Write down a roadmap for a proof of it by induction.
• Fill in the details of your roadmap to prove the statement.
(i) n! < n" for all n e N.
1
(ii) m3" > 100 × 2" for all n € N with n > 23. [You may use a calculator
100
for the base case.
- 6ak
Define the sequence (ak)kEN by a1 = 2, a2 = 5 and ak+2 =
for all k > 1. Then an = 2"-1 +3"-1 for all n > 1.
11
5ak+1
%3D
Expand
Transcribed Image Text

2. For each of the following statements • Write down a roadmap for a proof of it by induction. • Fill in the details of your roadmap to prove the statement. (i) n! < n" for all n e N. 1 (ii) m3" > 100 × 2" for all n € N with n > 23. [You may use a calculator 100 for the base case. - 6ak Define the sequence (ak)kEN by a1 = 2, a2 = 5 and ak+2 = for all k > 1. Then an = 2"-1 +3"-1 for all n > 1. 11 5ak+1 %3D

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