设bn=3/(anan+1),an=2n-51,tn是数列{bn}的前n项和,求使得Tn
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/21 19:35:39
设bn=3/(anan+1),an=2n-51,tn是数列{bn}的前n项和,求使得Tn
Tn
=b1+b2+...+bn
=(3/a1a2)+.+3/[ana(n+1)]
=3[1/a1a2+1/a2a3+...+1/ana(n+1)]
=3[1/(1*7)+1/(7*13)+...+1/(6n-5)(6n+1)]
=3{(1/6)(1-1/7)+(1/6)(1/7-1/13)+...+(1/6)[(1/6n-5)-1/(6n+1)]}
=(1/2)*[1-1/7+1/7-1/13+.+1/(6n-5)+1/(6n+1)]
=(1/2)*[1-1/(6n+1)]
因为n属于N*
所以1/(6n+1)>0
则:
Tn=(1/2)-(1/2)[1/(6n+1)]=10
所以
最小正整数m为10
=b1+b2+...+bn
=(3/a1a2)+.+3/[ana(n+1)]
=3[1/a1a2+1/a2a3+...+1/ana(n+1)]
=3[1/(1*7)+1/(7*13)+...+1/(6n-5)(6n+1)]
=3{(1/6)(1-1/7)+(1/6)(1/7-1/13)+...+(1/6)[(1/6n-5)-1/(6n+1)]}
=(1/2)*[1-1/7+1/7-1/13+.+1/(6n-5)+1/(6n+1)]
=(1/2)*[1-1/(6n+1)]
因为n属于N*
所以1/(6n+1)>0
则:
Tn=(1/2)-(1/2)[1/(6n+1)]=10
所以
最小正整数m为10
设bn=3/(anan+1),an=2n-51,tn是数列{bn}的前n项和,求使得Tn
设bn=3/(anan+1),an=6n-5,tn是数列{bn}的前n项和,求使得Tn
设bn=(an+1/an)^2求数列bn的前n项和Tn
an=3*2^(n-1),设bn=n/an求数列bn的前n项和Tn
已知数列{an}前n项和Sn=n^2+n,令bn=1/anan+1,求数列{bn}的前n项和Tn
数列bn的前n项和为Tn,6Tn=(3n+1)bn+2,求bn
Sn=n^2,令bn=1/anan+1,Tn是数列bn的前n项和,试证明Tn
已知数列{bn}中,点(bn,Tn)在直线y=-1/2x+1上,Tn是数列{bn}的前n项和,求Tn
已知数列an=4n-2和bn=2/4^(n-1),设Cn=an/bn,求数列{Cn}的前n项和Tn
数列{an}的前n项和为Sn=3an+2 设bn=n 求数列{an·bn}的和Tn
已知数列{an},{bn}满足a1=2,2an=1+anan+1,bn=an-1,设数列{bn}的前n项和为Sn,令Tn
数列an,满足Sn=n^2+2n+1,设bn=an*2^n,求bn的前n项和Tn