等差数列各项平方的和怎么算
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首项a1,公差d的等差数列各项平方的和
=a1²+(a1+d)²+(a1+2d)²+--------+[a1+(n-1)d]²
=na1²+[2+4+6+-------+2(n-1)]a1d+[1²+2²+3²+-----+(n-1)²]d²
=na1²+n(n-1)a1d+n(n-1)(2n-1)d²/6
=a1²+(a1+d)²+(a1+2d)²+--------+[a1+(n-1)d]²
=na1²+[2+4+6+-------+2(n-1)]a1d+[1²+2²+3²+-----+(n-1)²]d²
=na1²+n(n-1)a1d+n(n-1)(2n-1)d²/6
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首项a1,公差d的等差数列各项平方的和
=a1²+(a1+d)²+(a1+2d)²+--------+[a1+(n-1)d]²
=na1²+[2+4+6+-------+2(n-1)]a1d+[1²+2²+3²+-----+(n-1)²]d²
=na1²+n(n-1)a1d+n(n-1)(2n-1)d²/6
=a1²+(a1+d)²+(a1+2d)²+--------+[a1+(n-1)d]²
=na1²+[2+4+6+-------+2(n-1)]a1d+[1²+2²+3²+-----+(n-1)²]d²
=na1²+n(n-1)a1d+n(n-1)(2n-1)d²/6
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