(k+1)²=k²+2k+1,改变公式的写法,得(k+1)²- k²=2k+1.对上面的等式,依次令k=1,2,3,……,n,得2²-1²=2×1+1,3²-2²=2×2+1,4²-3²=2×3+1,……记S1=1+2+3+··+n,S1就等于n(n+1)除
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