一道初二数学计算题 3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+.+3/(x+20)(x+22)请写出过程,谢谢!
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一道初二数学计算题 3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+.+3/(x+20)(x+22)请写出过程,谢谢!
一道初二数学计算题 3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+.+3/(x+20)(x+22)
请写出过程,谢谢!
一道初二数学计算题 3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+.+3/(x+20)(x+22)请写出过程,谢谢!
3/[x(x+2)]=3/2*[1/x-1/(x+2)]
3/[(x+2)(x+4)]=3/2*[1/(x+2)-(1/(x+4)]
.
3/[(x+20)(x+22)]=3/2*[1/(x+20)-1/(x+22)]
把上面的式子相加：
3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+.+3/(x+20)(x+22)
=3/2[1/x-1/(x+22)]
=33/[x(x+22)]
=3/2 [1/x-1/(x+2)+1/(x+2)-1/(x+4)+...+1/(x+20)-1/(x+22)]
=3/2 [1/x-1/(x+22)]
=33/x(x+22)
3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+....+3/(x+20)(x+22)
=1.5[2/x(x+2)+2/(x+2)(x+4)+2/(x+4)(x+6)+....+2/(x+20)(x+22)]
=1.5[1/x-1/(x+2)+1/(x+2)-1/(x+4)+……+1/(x+20)-1/(x+22)]
=1.5[1/x-1/(x+22)]
=33/x(x+22)
注意到2/x(x+2)=1/x-1/(x+2),那么整个式子提取3/2，即
3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+....+3/(x+20)(x+22)
=(3/2) *[2/x(x+2)+2/(x+2)(x+4)+2/(x+4)(x+6)+....+2/(x+20)(x+22)]
=(3/2）*[1/x-1/(x+2)+1/(x+2)-1/...
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注意到2/x(x+2)=1/x-1/(x+2),那么整个式子提取3/2，即
3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+....+3/(x+20)(x+22)
=(3/2) *[2/x(x+2)+2/(x+2)(x+4)+2/(x+4)(x+6)+....+2/(x+20)(x+22)]
=(3/2）*[1/x-1/(x+2)+1/(x+2)-1/(x+4)+1/(x+4)-1/(x+6)+...+1/(x+20)-1/(x+22)]
=(3/2)*[1/x-1/(x+22)]
=(3/2)*[22/x(x+22)]
=33/[x(x+22)]
收起
由题意可得：
3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+....+3/(x+20)(x+22)
=3/2×[1/x-1/(x+2)+1/(x+2)-1/(x+4)+......+1/(x+20)-1/(x+22)]
=3/2×[1/x-1/(x+22)]
=33/[x(x+22)]
3/x(x+2)+3/(x+2)(x+4)+3/(x+4)(x+6)+....+3/(x+20)(x+22) =3/2[1/x-1/(x+2)+1/(x+2)-1/(x+4)+1/(x+4)-1/(x+6)+.....+1/(x+20)-1/(x+22)]=3/2[1/x-1/(x+22)]=33/x(x+22)