MA多伦多大学 MAT 137课业解析

MA多伦多大学 MAT 137课业解析

题意：

完成三道计算题

解析：

第三题： . For which positive integers n ≥ 1 does 2^n > n^2 hold? Prove your claim by induction.

证实：

n>=5

（1）当 n=5 时，2^5=32 > 5^2=25，不等式成立

（2）假设 n=k (k>5)时，2^k > k^2;

则 n = k+1 时，2(k+1)=22k > 2(k2)=(k-1)2-2+(k+1)^2 当k>5时，(k-1)^2-2>0 因此 2(k+1)>(k+1)2 即 n>5 时，假设成立 由数学概括法可知，V n>=5，2n>n2。

涉及知识点：

数学概括法，集合

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MAT 137Problem Set #1Due on Thursday September 26, 2019 by 11:59 pmSubmit via CrowdmarkInstructions• You will need to submit your solutions electronically. For instructions, see theMAT137 Crowdmark help page. Make sure you understand how to submit andthat you try the system ahead of time. If you leave it for the last minute and yourun into technical problems, you will be late. There are no extensions for any reason.• You will need to submit your answer to each question separately.• You may submit jointly written answers in groups of up to two people. Your partnercan be anyone in MAT137 from any lecture secti