数学数列问题bn=n²+n/4n²+12n+8,求bn前n项和
2019-05-30
数学数列问题
bn=n²+n/4n²+12n+8,求bn前n项和
优质解答
bn=n(n+1)/[4(n^2+3n+2)]
=n(n+1)/[4(n+1)(n+2)]
=(1/4)n/(n+2)
=(1/4)[1-2/(n+2)]
Sn=(1/4)[n-2(1/3+1/4+...1/(n+2))]
后面的是调和数列求和问题，要用到欧拉常数；
bn=n(n+1)/[4(n^2+3n+2)]
=n(n+1)/[4(n+1)(n+2)]
=(1/4)n/(n+2)
=(1/4)[1-2/(n+2)]
Sn=(1/4)[n-2(1/3+1/4+...1/(n+2))]
后面的是调和数列求和问题，要用到欧拉常数；