求和:1/1*4+1/4*7+1/7*10+...1/(3n-2)(3n+1)

问题描述:

求和:1/1*4+1/4*7+1/7*10+...1/(3n-2)(3n+1)

这个,感觉,题目是1/(1*4)+ 1/(4*7)+ .+ 1/(3n-2)(3n+1)吧,首先,我们看下,1/1-1/4 = 3/4,1/4 - 1/7 = 3/28,.1/(3n-2)- 1/(3n+1)= 3/(3n-2)(3n+1);所以,我们把原式变成1/3[1/1-1/4+1/4-1/7+.+1/(3n-2)- 1/...