x3 x4=5460y4 x5=4260
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按题设的规律,(6)=5*6*7,(7)=6*7*8,由等式知·=(7)/(6)+1=(6*7*8)/(5*6*7)+1=13/5
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)/21x2x3+2x3x4+3x4x5+.+7x8x9=2^3-2+3
2和3因为三个连续自然数至少有一个是偶数,且大于或等于2,所以它们的乘积一定是2的倍数三个连续自然数有一个是3的倍数,所以它们的乘积一定是3的倍数
解1/(1+2+3)+1/(2+3+4)+1/(3+4+5)……+1/(99+100+101)=1/6+1/9+1/12+1/15.+1/300=1/3*(1/2+1/3.+1/99+1/100)=1
1.解.裂项法.1/[n(n+1)(n+2)]=(1/2){1/[n)n+1)]-1/[(n+1)(n+2)]}=(1/2)[1/n-1/(n+1)-1/(n+1)+1/(n+2)]=(1/2)[1/
1×2×3+2×3×4+3×4×5+……+8×9×10=(1/4)(1×2×3×4)+(1/4)(2×3×4×5-1×2×3×4)+(1/4)(3×4×5×6-2×3×4×5)+……(1/4)(8×9
1x−1+1x+1+2xx2+1+4x3x4+1=2xx2−1+2xx2+1+4x3x4+1=4x3x4−1+4x3x4+1=8x7x8−1.故选D.
最简方法:拆项法n(n+1)(n+2)=1/4*[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]...2x3x4=1/4*[2x3x4*5-1*2x3x4]1x2x3=1/4*[
因为1x2x3=(1x2x3×4-0x1x2×3)/42x3x4=(2x3x4×5-1x2x3×4)/4.7x8x9=(7x8x9×10-6x7x8x9)/4所以1x2x3+2x3x4+3x4x5+…
原式=1/4(-0*1*2*3+1*2*3*4)+1/4(-1*2*3*4+2*3*4*5)+……+1/4[-(n-1)n(n+1)(n+2)+n(n+1)(n+2)(n+3)]=1/4[-0*1*2
1/2x3X4=(1/2X3-1/3X4)X1/21/3X4x5=(1/3X4-1/4X5)X1/2.1/8X9X10=(1/8X9-1/9X10)X1/2上述各式相加得:1/2x3X4十1/3X4x
设第n项为anan=n(n+1)(n+2)=n^3+3n^2+2n1×2×3+2×3×4+...+10×11×12=(1^3+2^3+...+10^3)+3(1^2+2^2+...+10^2)+2(1
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10=1-1/2-1/2(1-1/3)+1/2-1/3-1/2(1/2-1/4)+1/3-1/4-1/2(1/3-1
裂项求和1/((n-1)n(n+1))=(1/2)*(1/((n-1)n)-1/(n(n+1)))接着便可算了结果我算的是(1/2)*(1/6-1/(49*50))
根号28x29x30x31+1=28x31+1=869
(4)+(6)=3*4*5+5*6*7=60+210=270
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+1/3×4-1/4×5+1/4×5-1/5×6)=1/2×(1/1×2-1/5×6)=7/30
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+.+1/48x49x50=48*51÷(4*49*50)=306/1225
4x(n)x(n+1)+1=(2n+1)^2