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由k推向k十1是数学归纳法解题的关键一步,但李华证题不推就达到了k十1,从而创造了“不用归纳假设的数学归纳法。例子如下。题目:观察下列式子: (1~2十1)~(1/2)=(1·2)~(1/2)<2 (2~2十2)~(1/2)=(2·3)~(1/2)<3 (3~2十3)~(1/2)=(3·4)~(1/2)<4 ……问:由此可作出什么猜想,并用数学归纳
Pushing k from k to k is a key step in the mathematical inductive problem solving, but Li Hua’s problem is not pushed to k 1 and thus creates a mathematical induction method that does not require an inductive hypothesis. Examples are as follows. Title: Observe the following equations. : (1~2 10 1)~(1/2)=(1·2)~(1/2)<2 (2~2 10 2)~(1/2)=(2·3)~(1 /2)<3 (3~2 十3)~(1/2)=(3·4)~(1/2)<4 ...... Q: What conjecture can be made and summed up in mathematics?