(1)根据(2n+1)²-(2n-1)²=8n的规律.可得出400=()²-()²?(2)请用所学知识验证这个规律的正确性.
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![(1)根据(2n+1)²-(2n-1)²=8n的规律.可得出400=()²-()²?(2)请用所学知识验证这个规律的正确性.](/uploads/image/z/13384021-13-1.jpg?t=%EF%BC%881%EF%BC%89%E6%A0%B9%E6%8D%AE%EF%BC%882n%2B1%EF%BC%89%26%23178%3B-%EF%BC%882n-1%EF%BC%89%26%23178%3B%3D8n%E7%9A%84%E8%A7%84%E5%BE%8B.%E5%8F%AF%E5%BE%97%E5%87%BA400%3D%EF%BC%88%EF%BC%89%26%23178%3B-%EF%BC%88%EF%BC%89%26%23178%3B%3F%EF%BC%882%EF%BC%89%E8%AF%B7%E7%94%A8%E6%89%80%E5%AD%A6%E7%9F%A5%E8%AF%86%E9%AA%8C%E8%AF%81%E8%BF%99%E4%B8%AA%E8%A7%84%E5%BE%8B%E7%9A%84%E6%AD%A3%E7%A1%AE%E6%80%A7.)
(1)根据(2n+1)²-(2n-1)²=8n的规律.可得出400=()²-()²?(2)请用所学知识验证这个规律的正确性.
(1)根据(2n+1)²-(2n-1)²=8n的规律.可得出400=()²-()²?
(2)请用所学知识验证这个规律的正确性.
(1)根据(2n+1)²-(2n-1)²=8n的规律.可得出400=()²-()²?(2)请用所学知识验证这个规律的正确性.
400=(101)²-(99)²
根据平方差公式(2n+1)²-(2n-1)²
=(2n+1+2n-1)(2n+1-2n+1)
=4n*2=8n
(1). 400=8*50=(101)²-(99)²;
(2)(2n+1)²-(2n-1)²=(2n+1+2n-1)(2n+1-2n+1)=4n*2=8n