已知数列{an}满足a1+2a2+3a3+…+nan=n(n+1)(n+2),则它的前n项和Sn=?Sn=(3n^2+9n)/2_______

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 00:45:15
已知数列{an}满足a1+2a2+3a3+…+nan=n(n+1)(n+2),则它的前n项和Sn=?Sn=(3n^2+9n)/2_______已知数列{an}满足a1+2a2+3a3+…+nan=n(

已知数列{an}满足a1+2a2+3a3+…+nan=n(n+1)(n+2),则它的前n项和Sn=?Sn=(3n^2+9n)/2_______
已知数列{an}满足a1+2a2+3a3+…+nan=n(n+1)(n+2),则它的前n项和Sn=?
Sn=(3n^2+9n)/2_______

已知数列{an}满足a1+2a2+3a3+…+nan=n(n+1)(n+2),则它的前n项和Sn=?Sn=(3n^2+9n)/2_______
a1+2a2+3a3+…+nan=n(n+1)(n+2)
a1+2a2+3a3+…+(n-1)a(n-1)=(n-1)(n)(n+1)
两式相减,得
nan=3n(n+1)
an=3n+3
Sn=(a1+an)*n/2=(3n+9)n/2=(3n^2+9n)/2

a1+2a2+3a3+…+nan=n(n+1)(n+2), (1)
a1+2a2+3a3+…+(n-1)an-1=(n-1)(n+1)n (2)
(1)-(2)得:nan=n(n+1)(n+2-n+1)
an=3(n+1)
Sn=3n[2+n+1]/2=(3n^2+9n)/2

已知数列{an}满足a1+2a2+3a3+…+nan=n(n+1)(n+2),则a1+a2+a3+…+an=多少? 已知数列{an}满足:a1+a2+a3+.+an=n^2,求数列{an}的通项an. 已知数列an满足a1+2a2+3a3+……+nan=2^n,求an 已知数列{an}的前n项和为Sn 1若数列{an}是等比数列,满足2a1+a3=3a2.a3+2是a已知数列{an}的前n项和为Sn1若数列{an}是等比数列,满足2a1+a3=3a2.a3+2是a2.a4的等差中项,求数列{an}的通向公式 已知等比数列(an)满足2a1+a3=3a2且a3+2是a2,a4的等差中项 求数列(an)的通项公式? 已知数列{an}满足2a1+2^2a2+2^3a3+...+2^nan=4^n-1,则{an}的通项公式2a1+2^2a2+2^3a3就是2a1+4a2+8a3... 已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式 已知数列{an}满足a1=1,an=a1+2a2+3a3.+(n-1)an-1 (n>=2),则{an}的通项是什么 已知数列{an}满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1 (n≥2)求an=? 已知正数a1,a2,a3...an满足a1*a2*a3*...*an=1.求证:(2+a1)*(2+a2)*(2+a3)*...*(2+an)>=3^n (1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____(2)已知数列{an}满足a1=1,a1×a2×a3…an=n^2,求an. 已知等比数列{an}满足2a1+a3=3a2.且a3+2是a2.a4的等差中项.求数列已知等比数列{an}满足2a1+a3=3a2.且a3+2是a2.a4的等差中项. 求数列{an}的通项公式 设数列{an}的前n项和为sn,求S15 已知数列{an}满足:a1=1,an=a1+2a2+3a3+``````+(n-1)a(n-1)(n大于等于2),则通项公式an是什么? 已知数列an满足a1=1,an=a1+2a2+3a3+4a4+.(n-1)a(n-1),求通项an 已知数列{an}满足a1=1,an=a1+1/2a2+1/3a3+…+1/(n-1)an 已知数列{an}满足a1,a2-a1,a3-a2,...,an-an-1,...是首项为1,公比为1/3的等比数列.求an的表达式? 已知数列{an}满足a1=1;an=a1+2a2+3a3+...+(n-1)a(n-1)(n≥2);求通项公式 已知数列{an}满足:a1+2a2+3a3+...+nan=(2n-1)*3^n(n属于正整数)求数列{an}得通项公式