沿着前面的思路,这个公式的证明,其实是很自然也很容易的事: 我们在等式(n+1)2=n2+2n+1中,让n依次取从1开始的n个自然数:1,2,3,4,…,n,就得到n个相应的等式: 22=12+2×1+1, 32=22+2×2+1, 42=32+2×3+1, 52=42+2×4+1, …(n+1)2=n2+2n+1将这n个等式中等号两边的式子分别相加,相加时,注意消去等号左边与等号右边第一列中相同的数,就得到 Along the previous line of thought, the proof of this formula is actually very natural and easy: In equation (n+1)2=n2+2n+1, let n take the n natural numbers starting from 1 in order. :1,2,3,4,...,n, there are n corresponding equations: 22=12+2×1+1, 32=22+2×2+1, 42=32+2×3+ 1, 52=42+2×4+1, ...(n+1)2=n2+2n+1 Add the equations of the n equations on both sides of the equation. When adding, notice that the left side of the equal sign is eliminated. The same number as in the first column to the right of the equal sign