Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)

问题描述:

Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)

1/【(3n-2)(3n+1) 】
=1/3*【1/(3n-2)-1/(3n+1)】
所以Sn=1/3【1-1/4+1/4-1/7+1/7-.+1/(3n-2)-1/(3n+1)】
=1/3【1-1/(3n+1)】
=n/(3n+1)