设数列{an}的前n项和为Sn,若对任意的正整数n都有Sn=3an-5n(1)求数列{an}的首项,(2)求证数列{(an)+5}是等比数列,并求数列{an}的通项公式,(3)若数列{bn}满足bn=[(5n)+10]/(an)+5,且Tn=b
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设数列{an}的前n项和为Sn,若对任意的正整数n都有Sn=3an-5n(1)求数列{an}的首项,(2)求证数列{(an)+5}是等比数列,并求数列{an}的通项公式,(3)若数列{bn}满足bn=[(5n)+10]/(an)+5,且Tn=b
设数列{an}的前n项和为Sn,若对任意的正整数n都有Sn=3an-5n
(1)求数列{an}的首项,(2)求证数列{(an)+5}是等比数列,并求数列{an}的通项公式,(3)若数列{bn}满足bn=[(5n)+10]/(an)+5,且Tn=b1+b2+...+bn,求证
Tn
设数列{an}的前n项和为Sn,若对任意的正整数n都有Sn=3an-5n(1)求数列{an}的首项,(2)求证数列{(an)+5}是等比数列,并求数列{an}的通项公式,(3)若数列{bn}满足bn=[(5n)+10]/(an)+5,且Tn=b
(1)当n=1时,a1=3a1-5
a1=5/2
(2)S(n+1)=3a(n+1)-5(n+1)
S(n+1)-Sn=3a(n+1)-3an-5(n+1)+5n
a(n+1)=3a(n+1)-3an-5
a(n+1)=3/2an+5/2
a(n+1)+X=3/2(an+5/3+2/3X)
令 x=5/3+2/3x
x=5
a(n+1)+5=3/2an+5/2+5=3/2(an+5)
叠乘法
an+5=(3/2)^(n-1) *(a1+5)=(3/2)^(n-1)*(15/2)
an=((3/2)^n * 5)-5
(3)题目是bn==[(5n)+10]/((an)+5)
则bn=(2/3)^n * (n+2)
Sn=(2/3)*3+4*(2/3)^2+……+(2/3)^n * (n+2)
(2/3)Sn=3*(2/3)^2+……+(2/3)^n * (n+1)+(2/3)^(n+1) * (n+2)
(1/3)Sn==(2/3)*3+(2/3)^2+……+(2/3)^n+ (2/3)^(n+1) * (n+2)
Sn=4+(6 - 3^n/2^n)+(2/3)^(n+1) *(n+1)
3^n/2^n>1,(2/3)^(n+1) *(n+1)