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我正在尝试为明天的测试学习归纳证明。我试图理解书中问题的解决方案,但我的数学有点生疏。有人可以解释这些都是平等的吗?我不明白如何从第一个方程中找到最后一个方程。
n(n+1)/2 + (n+1) = n(n+1) + 2(n+1)/2 = (n+1)(n+2)/2
因式分子。
(n^2 + n + 2n + 2)/2 = (n^2 + 3n + 2)/2 = ((n+1)(n+2))/2
第一个是,
n(n+1)/2 + (n+1) ( n(n+1)+2(n+1) )/2 ( (n+1)(n+2) ) /2
知道了?
最后的/2对两者都很常见。