数列{ an}{ bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n若{ an}为等差数列,求证数列{ bn}也是等差数列
来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/15 19:41:53
数列{an}{bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n若{an}为等差数列,求证数列{bn}也是等差数列数列{an}{bn}满足关系式bn=1*a1+2*a2+
数列{ an}{ bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n若{ an}为等差数列,求证数列{ bn}也是等差数列
数列{ an}{ bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n
若{ an}为等差数列,求证数列{ bn}也是等差数列
数列{ an}{ bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n若{ an}为等差数列,求证数列{ bn}也是等差数列
证明:若{ an}为等差数列,设公差为d,则
b[n]={(1+2+……+n)*a1+[1*2+2*3+……+(n-1)n]d}/(1+2+……+n)
=a1+(1^2+2^2+3^2+……+n^2)d-(1+2+……+n)d/(1+2+……+n)
=a1+[n(n+1)(2n+1)d/6-n(n+1)d/2]/[n(n+1)/2]
=a1+(2n+1)d/3-d
=a1+(2n-2)d
a1+(n-1)*2d
显然,b[n]是以a1为首项,2d为公差的等差数列.命题得证.
要求的是啥哈?
数列{an}为等差数列,数列{bn}满足bn=2an+1+a2n-1,证明{bn}为等差数列
已知数列{an}、{bn}满足:a1=1/4,an+bn=1,bn+1=bn/1-an^2.求{bn}通项公式
数列{ an}{ bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n,若{bn}为等差数列,求证数列{an}也是等差数
数列{ an}{ bn}满足关系式bn=1*a1+2*a2+3*a3…+nan/1+2+3+…+n若{ an}为等差数列,求证数列{ bn}也是等差数列
已知数列(an )和(bn )满足下列关系式:bn =n 分之a1+a2+a3+…+an 若bn =n的平方,求数列(an )...已知数列(an )和(bn )满足下列关系式:bn =n 分之a1+a2+a3+…+an若bn =n的平方,求数列(an
已知数列(an )和(bn )满足下列关系式:bn =n 分之a1+a2+a3+…+an 若bn =n的平方,求数列(an )...已知数列(an )和(bn )满足下列关系式:bn =n 分之a1+a2+a3+…+an若bn =n的平方,求数列(an
已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列bn的前20项之和.
已知数列{an}、{bn}满足:a1=1/4,an+bn=1,bn+1=bn/1-an^2 (1)求{an}的通项公式
数列{an}中,a1=-60,an+1=an+3,若数列{bn}满足bn=|an|,求数列{bn}前30项和
已知数列{an},{bn}满足a1=2,2an=1+2an*an+1,设{bn}=an-1求数列{1n}为等差数列急!!!
设数列{an}满足下列关系式a1=2a (a是不为0的常数)an =2a - a^2 / an-1 数列bn=1/(an-a)证明{bn}为等差数列
设数列{an}满足下列关系式a1=2a (a是不为0的常数)an =2a - a^2 / an-1 数列bn=1/(an-a),求{bn}都通项公式
数列{an}与{bn}满足an=1/n(b1+b2+…+bn)(n∈N).求证:数列{bn}为等差数列的充要条件是数列{an}为等差数列
已知等差数列{an}满足a2=3,a5=9,若数列{bn}满足b1=3,bn-1=a下标bn则bn为?
数列an及正项数列bn满足:a1=0.5,a(n+1)=1除以1+bn,an+bn=1,求bn的通项公式,比较ln(1+bn)与bn的大小
数列an,bn满足a1=b1=1,an+1-an=bn+1/bn=2,则数列ban的前10项和为
an=2*3^n-1 若数列bn满足bn=an+(-1)^n*ln(an),求数列bn前n项和Sn
已知数列an满足bn=an-3n,且bn为等比数列,求an前n项和Sn