kgdc.net
当前位置:首页 >> 1x2+2x3+3x4 >>

1x2+2x3+3x4

=1*(1+1)+2*(2+1)+…+99*(99+1) =1²+…+99²+1+…+99 =99*(99+1)(2*99+1)/6+99*(99+1)/2 =33*50*199+33*50*3 =33*50*202 =333300

n*(n+1)=n*n+n 1*1+2*2+...n*n= n(n+1)(2n+1)/6 原式=(1+2+....+n)+(1*1+2*2+...n*n) =n(n+1)(2n+1)/6 + n(n+1)/2

因为n(n+1)=n平方+n 原式=(1平方+2平方+……n平方)+(1+2+3……n) =n(n+1)(2n+1)/6+n(n+1)/2为标准答案 注:Sn(1平方+2平方+……n平方)的证明: (a+1)³-a³=3a²+3a+1(即(a+1)³=a³+3a²+3a+1) a=1时:2³...

n(n+1) =(1/3) { n(n+1)(n+2) - (n-1)n(n+1) } 1x2+2x3+3x4+...99x100 = 1x2 + (1/3) { (2x3x4 - 1x2x3) + (3x4x5 - 2x3x4) +...+(99x100x101 - 98x99x100) } = 1x2 + (1/3) { 99x100x101 -1x2x3 } = (1/3) 99x100x101 =333300

1x2+2x3+3x4+…+n(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1) =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)[(2n+1)+3]/6 1x2+2x3+3x4+…+10x11 =10x(10+1)x[(10x2+1)+3]/6 =110x4 =440

一般的,有: (n-1)n(n+1) =n^3-n {n^3}求和公式:Sn=[n(n+1)/2]^2 {n}求和公式:Sn=n(n+1)/2 1x2x3+2x3x4+3x4x5+....+7x8x9 =2^3-2+3^3-3+...+8^3-8 =(2^3+3^3+...+8^3)-(2+3+...+8) =[(8*9/2)^2-1]-8*9/2+1 =1260

把每项的乘都先看成是n×(n+1),然后拆开成n×n+n。 那么式子就变成(1×1+1)+(2×2+2)+(3×3+3)+(4×4+4)+......+(49×49+49),再把1到49的平方和放一起计算,1到49的和放一起计算。 1到n的平方和有公式:n×(n+1)×(2×n+1)/6,n等于49,...

1X2=1*1+1 ... N(N+1)=N^2+N 所以1*2+2*3+.....+N*(N+1) =1^2+2^2+....+N^2+(1+2+3+....+N) =N*(N+1)(2N+1)/6+N(N+1)/2 =N(N+1)(2N+1+3)/6=N(N+1)(N+2)/3 3x(1x2+2x3+3x4+......+99x100)=3(99*100*101/3) =99*100*101=999900

1x2+2x3+3x4+…+100x(100+1) =1^2+1+2^2+2+3^2+3+...+100^2+100 =(1^2+2^2+3^2+...+100^2)+(1+2+3+...+100) =100*(100+1)(2*100+1)/6+100*(100+1)/2 =100*101+102/3 =343400 如果不懂,请追问,祝学习愉快!

1x2+2x3+3x4+...+10x11 =2+6+12+20+30+42+56+72+90+110 =440

网站首页 | 网站地图
All rights reserved Powered by www.kgdc.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com