如果是要問Excel怎么計(jì)算,那就按樓上說的做.
如果是當(dāng)成數(shù)學(xué)題就按下面方法做.
令Sn=1²+2²+3²+……+n²
由n²=n(n+1)-n有
Sn=1²+2²+3²+……+n²
=1*2-1+2*3-2+……+n(n+1)-n
=1*2+2*3+……+n(n+1)-(1+2+……+n)
由于n(n+1)={ n(n+1) [(n+2)-(n-1)] }/3=[n(n+1)(n+2)-(n-1)n(n+1)]/3,所以
1*2+2*3+...+n(n+1)
=[1*2*3-0 + 2*3*4-1*2*3 + ……+ n(n+1)(n+2)-(n-1)n(n+1) ]/3
=[n(n+1)(n+2)]/3
所以
Sn=1²+2²+3²+.+n²
=[n(n+1)(n+2)]/3 - [n(n+1)]/2
=n(n+1)[(n+2)/3-1/2]
=n(n+1)[(2n+1)/6]
=n(n+1)(2n+1)/6
所以 原題=Sn-1=n(n+1)(2n+1)/6-1