是求和的,求和的,Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 09:57:54
是求和的,求和的,Sn=1/1·4+1/4·7+...+1/(3n-2)(3n+1)是求和的,求和的,Sn=1/1·4+1/4·7+...+1/(3n-2)(3n+1)是求和的,求和的,Sn=1/1·

是求和的,求和的,Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)
是求和的,求和的,
Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)

是求和的,求和的,Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)
列项相消法
Sn=1/1·4 + 1/4·7 +...+1/(3n-2)(3n+1)
=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+...+(1/3)* (1/(3n-2)-1/(3n+1))
=(1/3)(1-1/4+1/4-1/7+...+1/(3n-2)-1/(3n+1)
=(1/3)(1-1/(3n+1))
=1/3 * 3n/(3n+1)
=n/(3n+1)

Sn=1/3*(1-1/4+1/4-1/7+...+1/(3n-2)-1/(3n+1))
=1/3*(1-1/(3n+1))
=1/3*3n/(3n+1)
=n/(3n+1)
裂项相消...