2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
HW#8 (SP 22)
截止时间 3月24日 23:59 得分 90 问题 9
可用 3月18日 0:00 至 3月24日 23:59 7 天 时间限制 无
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此测验锁定于 3月24日 23:59。
最新 尝试 1 522 分钟 55，满分 90 分
正确答案已隐藏。
此测验的分数: 55，满分 90 分 提交时间 3月24日 23:59 此尝试进行了 522 分钟。
Prove the following by using the principle of mathematical induction for all :
is divisible by 3.
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2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Show that for .
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2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
For any and any , prove that .
Use the Principle of Mathematical Induction to verify that, for any positive integer, is divisible by .
Prove the following by using the principle of mathematical induction
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2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
the proof is correct but the structure is partially incorrect
Fibonacci numbers are defined as follows: We have Prove the following using induction:
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2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
From : Incomplete
Let be the sequence defined by
for . Prove that
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2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Use strong induction to show that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers , and so on. [Hint: For the inductive step, separately consider the case where is even and where it is odd. When it is even, note that is an integer.]
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2022/4/28 21:26 HW#8 (SP 22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Assume we know that for each natural number , there is a prime number such that . We call such a prime number a
number. Prove that every natural number
can be written as the summation of distinct pseudo-prime numbers
(The sum can consist of only one element).
测验分数: 55，满分 90 分
please write in proper prove structure next time
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