计算1/1*2+1/2*31/3*4+1/4*5+1/5*6计算1/1*3+1/3*5+1/5*7+1/7*9+1/9*11化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+1/(x+9)(x+12)
计算1/1*2+1/2*31/3*4+1/4*5+1/5*6
计算1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+1/(x+9)(x+12)
计算1/1*2+1/2*31/3*4+1/4*5+1/5*6计算1/1*3+1/3*5+1/5*7+1/7*9+1/9*11化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+1/(x+9)(x+12)
计算1/1*2+1/2*31/3*4+1/4*5+1/5*6
计算1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+1/(x+9)(x+12)
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)
做这题之前请看下面一些式子:
1/(1×2)=1-(1/2)=1/2
1/(2×3)=(1/2)-(1/3)=1/6
1/(3×4)=(1/3)-(1/4)=1/12
…………
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)
原式=1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+(1/5)-(1/6)
=1-(1/6)
=5/6
1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
1/3*5=0.5×[(1/3)-(1/5)]
1/5*7=0.5×[(1/5-1/7)]……………
∴1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
原式=0.5[1-(1/3)+(1/3)-(1/5)+(1/5)-……-(1/9)+(1/9)-(1/11)]
=0.5×[1-(1/11)]
=0.5×(10/11)
=5/11
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+1/(x+9)(x+12)
1/x(x+3)=1/3{(1/x)-[1/(x+3)]}
1/(x+3)(x+6)=1/3{[1/(x+3)]-1/(x+6)}…………
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+1/(x+9)(x+12)
原式=1/3{(1/x)-[1/(x+3)]+[1/(x+3)]-[1/(x+6)]+[1/(x+6)]-………-[1/(x+9)]+[1/(x+9)]-[1/(x+11)]}
=1/3{(1/x)-[1/(x+11)]}
=1/3[(x+10)/(x²+11x)]
=(x+10)/(3x²+33x)