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:作业帮 时间:2024/08/06 14:00:33
计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)
x){nuӍ LḾak "4\#WP&Hv6ۏ*dk@}07ʘhjY&@9edhj?jXDBLj׆jֆia!q>, @a/g

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)