ldcf.net
当前位置:首页 >> 请计算1/(x%1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5)... >>

请计算1/(x%1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5)...

裂项相消原理 1/(x-1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5) =1/2[1/(x-1)-1/(x+1)+1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)] =1/2[1/(x-1)-1/(x+5)] =1/2(x+5-x+1)/(x-1)(x+5) =3/(x-1)(x+5) 或者直接算 =[(x+3)(x+5)+(x-1)(x+5)+(x-1)(x+1)]/(x-1)(x+1)...

原式=(1-x+x+1)/(1+x)(1-x) =2/(1-x²)

您好: 1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3) =1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3) =1x-1/(x+3) =3/x(x+3) 如果本题有什么不明白可以追问,如果满意记得采纳 如果有其他问题请采纳本题后另发点击向我求助,答题不易,请谅解,谢谢。 祝...

1/x(x+1) + 1/(x+1)(x+2) + 1/(x+2)(x+3) +.......+1/(x+2010)(x+2011) =1/x-1/(x+1) + 1/(x+1)-1/(x+2) + 1/(x+2)-1/(x+3) +.......+1/(x+2010)-1/(x+2011) =1/x-1/(x+2011) =2011/x(x+2011)

2/[(x+1)(x+3)]+2/[(x+3)(x+5)]+……+2/[(x+2013)(x+2015)] =[1/(x+1)-1/(x+3)]+[1/(x+3)-1/(x+5)]+……+[1/(x+2013)-1/(x+2015)] =1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+……+1/(x+2013)-1/(x+2015) =1/(x+1)-1/(x+2015) =[(x+2015)-(x+1)]/[(x+1)(x+2015...

1/(x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2) =(x-1)/(x-2)(x-3)(x-1)-2(x-2)/(x-1)(x-2)(x-3)+(x-3)/(x-1)(x-2)(x-3) =【x-1-2x+4+x-3】/(x-1)(x-2)(x-3) =【0】/(x-1)(x-2)(x-3) =0

3(X+1)-1/3(X-1)=2(X+1)-1/2(X-1) 移项,得 (3-2)(x+1)=(1/3-1/2)(x-1) x+1=-1/6(x-1) 同乘以6得 6x+6=1-x 7x=-5 x=-5/7

1/(x+3)(x+4)+1/(x+4)(x+5)......1/(x+99)(x+100) =1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)+......+1/(x+99)-1/(x+100) =1/(x+3)-1/(x+100) =(x+100)/[(x+3)(x+100)]-(x+3)/[(x+3)(x+100)] =(x+100-x-3)/[(x+3)(x+100)] =97/[(x+3)(x+100)]

(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4) =(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)×(1/2+1/3+1/4) =(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4) =1/5

原式 =[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)] +[1/(x+3)-1/(x+4)]+[1/(x+4)-1/(x+5)] =1/(x+1)-1/(x+5) =[(x+5)-(x+1)]/[(x+1)(x+5)] =4/(x^2+6x+5)

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