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数列求和(五)

112+123+134++1n(n+1)=11n+1=nn+1

1123+1234+1345++1n(n+1)(n+2) =1412(n+1)(n+2)

11234+12345+13456++1n(n+1)(n+2)(n+3) =11813(n+1)(n+2)(n+3)

nj=21(j+1)(j1)=nj=21j21=3412n12(n+1)

nj=11(2j+1)(2j1)=n2n+1

nj=11(3j2)(3j+1)=n3n+1

nj=11(2j1)(2j+1)(2j+3)=11214(2n+1)(2n+3)

nj=11(3j2)(3j+1)(3j+4)=12416(3n+1)(3n+4)



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参阅
  1. 数学 - 数学符号 - 数学索引
  2. 手册 = 初中数学手册 + 高中数学手册 + 数学手册 + 实用数学手册
  3. 初等数学 = 小学数学 + 中学数学 ( 初中数学 + 高中数学 )
  4. 高等数学 = 基础数学 ( 代数 + 几何 + 分析 ) + 应用数学
  5. 公式 - 定理 - - 函数图 - 曲线图 - 平面图 - 立体图 - 动画 - 画画
  6. 书单 = 数学 + 物理 + 化学 + 计算 + 医学 + 英语 + 教材 - QQ群下载书
  7. 数学手册计算器 = 数学 + 手册 + 计算器 + 计算机代数系统
  8. 检测 - 例题 :

d0.5ydx0.5=sin(x-1)sin(y-1) == ? d0.5ydx0.5-cosh(y)-sinh(y)=0 == ? d1.6ydx1.6-y(x)(dx)0.8-y-exp(x)=0 == ? y(x)(dx)0.5-y-exp(x)=0 == ? d0.5ydx0.5-exp(y)x=0 == ? d0.5ydx0.5-exp(y)y=0 == ? d0.5ydx0.5=cos(x)xy == ? ydy0.5dx0.5-x-1=0 == ? d1.2ydx1.2-2d0.6ydx0.6+y-exp(x)=0 == ? d0.5ydx0.5=cos(y)exp(x)x == ? d1.6ydx1.6-2d0.8ydx0.8+y-exp(x)=0 == ? d0.5ydx0.5-exp(y)x=0 == ? d1.6ydx1.6-3d0.8ydx0.8+2y-exp(x)=0 == ? d0.5ydx0.5 +log(y-1)-exp(x)-x=0 == ? d0.5ydx0.5-exp(y)sin(x)=0 == ? d0.5ydx0.5=ysin(x)x == ? y(0.5)(x)-4exp(x)y-exp(x)=0 == ? dy0.5dx0.5=1x-y == ? dydx-d0.5ydx0.5 - y - exp(x)=0 == ? dydx-exp(y-1)-x-x2=0 == ? d1.2ydx1.2-3dy0.6dx0.6+2y-exp(x)=0 == ? dydx-d0.5ydx0.5-y-1=0 == ? d0.5ydx0.5-cos(y)sin(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(4x)=0 == ? dydx-exp(y-1)-exp(x)=0 == ? dydx-2d0.5ydx0.5-y-exp(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(x)=0 == ? d0.5ydx0.5-e4x-y=0 == ? y(0.5)(x)-exp(x)y-exp(x)=0 == ? y(0.5)(x)-exp(x)y-4exp(x)=0 == ? dydx-3d0.5ydx0.5+2y-exp(x)=0 == ? yd0.5ydx0.5-x-1=0 == ? y(1)(x)-exp(y-1)-x=0 == ? d1.6ydx1.6-d0.8ydx0.8-2y-exp(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(4x)=0 == ? d0.5ydx0.5-log(y-1)-exp(x)+x=0 == ? dydx+asin(y-1)-cos(x)-x=0 == ? d1.6ydx1.6-3d0.8ydx0.8+2y-exp(x)=0 == ? dydx-y-1-x-1=0 == ? dydx-exp(y-1)-exp(x)=0 == ? dydx +asinh(y-1)-cosh(x)-x =0 == ? (d12ydx12)2-3ydy0.5dx0.5+2y2=0 == ? dy0.5dx0.5=cos(x)cos(y-1) == ? d0.5ydx0.5+log(y-1)-exp(x)-x=0 == ? dy0.5dx0.5=sin(x-1)exp(y-1) == ? yd2ydx2-(dydx)2+1=0 == ? y(1)(x)-exp(y-1)-log(x)=0 == ? d2ydx2exp(x)-exp(y-1)=0 == ? d1.6ydx1.6-2d0.8ydx0.8-y-exp(x)=0 == ? d1.6ydx1.6-2d0.8ydx0.8+y-exp(x)=0 == ? dydx-3d0.5ydx0.5+2y-exp(x)=0 == ? y(0.5)(x)-xy-x=0 == ? ydy3dx3-x3-3x2-3x-1=0 == ? y(1.8)(x)-2y(0.9)(x)+y-1=0 == ? y(0.5)(x)=1xy-1 == ? y(2)(x)y2-x2-2x-1=0 == ? (d0.5ydx0.5)2-5d0.5ydx0.5+6=0 == ? y(0.5)(x)-2exp(x)y-4exp(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(x)=0 == ? y0.5(x)=2yexp(x) == ? y(0.5)(x)-exp(x)y2=0 == ? d1.6ydx1.6-2d0.8ydx0.8+y-exp(x)=0 == ? y(1)(x)-y2-xy=0 == ? y(1)(x)-y(0.5)(x)-y-1=0 == ? y(2)(x)-y2-x2=0 == ? y^((2))(x) -y^2-x^2-2x*y=0 == ? y^((0.5))(x) -int y(x) (dx)^0.5-y-exp(x)=0 == ? d^0.5/dx^0.5 y -2cos(y)*exp(x)=0 == ? d^0.5/dx^0.5 y -4sin(y)*exp(x)=0 == ? (d^0.5y)/dx^0.5=sin(x^2)*y == ? (d^0.5y)/dx^0.5-sin(x)*sin(y)=0 == ? (d^0.5y)/dx^0.5-sinh(x)*sinh(y)=0 == ? y^((1))(x)=exp(x-y)-x == ? x*(d^0.5y)/dx^0.5-y-2x=0 == ? (d^0.5y)/dx^0.5=sinh(x-1)*sinh(y-1) == ? y^((0.5))(x)-exp(-x)*y^2=0 == ? (d^0.5y)/dx^0.5=y/x*sin(x) == ? (dy)/dx-sin(x-y)-1=0 == ? (d^2.5y)/dx^2.5=y*(d^0.5y)/dx^0.5 == ? (d^0.5y)/dx^0.5=y*(dy)/dx == ? (d^(2-i)y)/dx^(2-i)- y+x=0 == ? (d^2y)/dx^2=y^3*x^2 == ? y*(d^2y)/dx^2-x^2-3x-1=0 == ? y*(d^2y)/dx^2-2x^2-3x-1=0 == ? (y-x-1)*(d^2y)/dx^2-3x-1=0 == ? y^2*(d^2y)/dx^2-x^2-4x-4=0 == ? (y-x-1)*(d^2y)/dx^2-x^2-4x-4=0 == ? y*(d^2y)/dx^2-2x^2-2x-1=0 == ? y*(d^3y)/dx^3-6x^3-3x^2-3x-1=0 == ? y^((0))(x)*y^((1))(x)*y^((2))(x)=x^2 == ? y^((3))(x)*y^((2))(x)=y^((1/2))(x) == ? y^((3))(x)=exp(x)*y^((1))(x)*y^((1/2))(x) == ? y^((1/2))(x)*y^((3))(x)=exp(x) == ? y^((1/2))(x)*y^((2))(x)=exp(x) == ? (d^0.5y)/dx^0.5-2x*y-1=0 == ? y^2*(d^0.5y)/dx^0.5-x^2-4x-4=0 == ? exp(y-1)*(d^0.5y)/dx^0.5-x=0 == ? y*(d^2y)/dx^2-(x-2)*(2x-4)=0 == ? y*(d^3y)/dx^3-6x^3-4x^2-4x-1=0 == ? exp(y-1)*(d^2y)/dx^2-exp(x)=0 == ? y^2*(d^2y)/dx^2-x^2-1=0 == ? 1/y^2*(d^2y)/dx^2-x^2-1=0 == ? (y-x-1)*(d^3y)/dx^3-(x-2)*(2x-4)*(3x-1)=0 == ? (d^0.5y)/dx^0.5-2x^2*y^2-8x^2=0 == ? (d^0.5y)/dx^0.5-2x*y^2-8x=0 == ? (d^0.5y)/dx^0.5-y^2-2y-2=0 == ? (d^0.5y)/dx^0.5-log(y-1)*exp(x)=0 == ? y*(d^2y)/dx^2-(dy/dx)^2-1=0 == ? (d^2y)/dx^2-asin(y-1)-sin(x)-x=0 == ? dy/dx*(x--y)-x--y-1 = 0 == ?


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