数列{an}的前n项的和Sn=n2-10n(n属于N*),数列{bn}满足bn=(an+1)/an(n属于N*),(1)
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数列{an}的前n项的和Sn=n2-10n(n属于N*),数列{bn}满足bn=(an+1)/an(n属于N*),(1)
判断数列 {an}是否为等差娄列,并证明你的结论;
(2)求数列{bn}中值最大的项和值最小的项
(3)Cn=绝对值an,求数列前n项和Tn
判断数列 {an}是否为等差娄列,并证明你的结论;
(2)求数列{bn}中值最大的项和值最小的项
(3)Cn=绝对值an,求数列前n项和Tn
(1)
Sn =n^2-10n
an = Sn -S(n-1)
= (2n-1) -10
= 2n-11
=>{an}是等差娄列
(2)
bn = (an+1)/an
= (2n-10)/(2n-11)
max bn = b1 = 8/9
min bn = b5 =0
(3)
an > 0
2n-11 >0
n > 11/2
n= 6
cn =|an|
for n =6
Tn = -(a1+a2+..+a5) +(a6+a7+..+an)
=25 + (2n-11+1)(n-5)/2
=25 + (n-5)^2
=n^2-10n +50
Sn =n^2-10n
an = Sn -S(n-1)
= (2n-1) -10
= 2n-11
=>{an}是等差娄列
(2)
bn = (an+1)/an
= (2n-10)/(2n-11)
max bn = b1 = 8/9
min bn = b5 =0
(3)
an > 0
2n-11 >0
n > 11/2
n= 6
cn =|an|
for n =6
Tn = -(a1+a2+..+a5) +(a6+a7+..+an)
=25 + (2n-11+1)(n-5)/2
=25 + (n-5)^2
=n^2-10n +50
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