计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 01:49:50
计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-

计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)
计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)

计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)
3/(3n-2)(3n+1)=1/(3n-2)-1/(3n+1)
原式=(1/1-1/4)+(1/4-1/7)+(1/7-1/10)+……+[1/(3n-2)-1/(3n+1)]
=1/1-1/4+1/4-1/7+1/7-1/10+……+1/(3n-2)-1/(3n+1)
=1-1/(3n+1)
=3n/(3n+1)