Question

1×2的平方加上2×3的平方加上3×4的平方一直加到19×20的平方怎么算

Answer 1

把1写成2-1，把2写成3-1，依次，19为20-1.利用乘法分配律，得式变为：2的三次方一直加到20的三次方，再减去2的平方加到20的平方的和，利用三次方求和公式和二次方求和公式即可。

Answer 2

这道题可以运用错位相减法，
an
= n(n+1)^2
= n(n+1)(n+2) - n(n+1)
= (1/4)[ n(n+1)(n+2)(n+3) -(n-1)n(n+1)(n+2) ] -(1/3)[ n(n+1)(n+2) -(n-1)n(n+1) ]

Sn
=a1+a2+...+an
=(1/4)n(n+1)(n+2)(n+3) - (1/3)n(n+1)(n+2)
=(1/12)n(n+1)(n+2)(3n+5)

1x2^2+2x3^2+...+19x20^2
=S19
=(1/12)(19)(20)(21)(62)
=41230
希望对你有帮助，望采纳谢谢

Answer 3

an
= n(n+1)^2
= n(n+1)(n+2) - n(n+1)
= (1/4)[ n(n+1)(n+2)(n+3) -(n-1)n(n+1)(n+2) ] -(1/3)[ n(n+1)(n+2) -(n-1)n(n+1) ]

Sn
=a1+a2+...+an
=(1/4)n(n+1)(n+2)(n+3) - (1/3)n(n+1)(n+2)
=(1/12)n(n+1)(n+2)(3n+5)

1x2^2+2x3^2+...+19x20^2
=S19
=(1/12)(19)(20)(21)(62)
=41230

Answer 4

Sn=2³+3³+……（n+1）³-（2²+3²+……（n+1）²）
=1³+2³+3³+……（n+1）³-（1²+2²+3²+……（n+1）²）
=（（n+2）(n+1)/2)²-（n+1）(n+2)(2n+3)/6

S19=41230

Answer 5