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从不同角度、不同层面,运用构造思想与方法来探究公式sum from i=1 to n i~2=(n(n+1)(2n+1))/6 的推证方法,对于深入认识事物的本质、锻炼思维品质、培养创新能力,具有不可低估的作用.请看: 1.构造恒等式 方法1 运用数的特征进行联想,引入高一次恒等式 (k+1)3=k3+3k2+3k+1(k=1,2,…,n),得 (k+1)3-k3=3k2+3k+1. 令k=1,2,…,n,递推迭加有
From different perspectives and levels, we use structural ideas and methods to explore the method of formula sum from i=1 to ni~2=(n(n+1)(2n+1))/6 to understand things in depth. The essence, the quality of exercise thinking, and the ability to cultivate innovation have a role that cannot be underestimated. See: 1. Constructing identity method 1 Using the features of numbers to associate, introduce a high identity (k+1)3=k3+3k2+3k+1 (k=1,2,...,n), get (k+1)3-k3=3k2+3k+1. Let k=1,2,...,n, recursively superimpose