Question

求数学题解法

1的4次方加2的四次方加到100的四次方再除以1²＋2²＋3²＋…100²＝？

Answer 1

题目还是写成分数形式，分子分母分开来看吧

分子：1^4 +2^4 +3^4 +4^4 +……+ 100^4，四次方其实就是二次方的平方
= (1")"+(2")"+(3")"+(4")"+……+(99")"+(100")"
= (1")"+(2")"-2(2")(1")+2(1")(2") +(3")"+(4")"-2(4")(3")+2(3")(4")+……+(99")"+(100")"-2(100")(99")+2(99")(100")
= (2"-1")"+2(1X2)" +(4"-3")"+2(3X4)" +……+(100"-99")"+2(99X100)"

= (2+1)"+2(1X2)" +(4+3)"+2(3X4)" +……+(100+99)"+2(99X100)"
= 1"+2"+ 2X1X2+ 2(1X2)"+ 3"+4"+ 2X3X4+ 2(3X4)"+……+ 99"+100"+ 2X99X100+ 2(99X100)"
=[1"+2"+3"+4"+……+99"+100"]+ 2X[(1X2)"+1X2 +(3X4)"+3X4 +……+(99X100)"+99X100]

=分母+ 2X[1X2 +3X4 +……+ 99X100]+ 2X[(1X2)"+(3X4)"+……+(99X100)"]
=分母+ [1X(1+1)+(2-1)X2 +3X(3+1)+(4-1)X4 +……+99(99+1)+(100-1)X100]+ [(1"+1)"+(2"-2)"+(3"+3)"+(4"-4)"+……+(99"+99)"+(100"-100)]
=分母+ [1"+1 +2"-2 +3"+3 +4"-4 +……+ 99"+99 +100"-100]+ [1+2+1 +(2")"-2X2(2")+2"+……+(99")"+2X99(99")+99"+(100")"-2X100(100")+100"]

=分母+[分母+1-2+3-4+……+99-100]+[分母+1+2+(2")"-2X2(2")+(3")"+2X3(3")+(4")"-2X4(4")+……+(99")"+2X99(99")+(100")"-2X100(100")]
=分母X3 +(-1)X50 +[2+1+(2")"-2X2(2")+(3")"+2X3(3")+(4")"-2X4(4")+……+(99")"+2X99(99")+(100")"-2X100(100")

Answer 2

直接插入图片怎么不行？还要打字，真哆嗦。