设Sn是正项数列an的前n项和,且Sn=1/4an^2十1/2an一3/4

中文asd 1年前 已收到2个回答 举报

甜鸭蛋 幼苗

共回答了19个问题采纳率:94.7% 举报

(1)
Sn=(1/4)(an)^2+(1/2)an-3/4
n=1,
(a1)^2-2an-3=0
(a1-3)(a1+1)=0
a1=3
an = Sn -S(n-1)
= (1/4)[(an)^2 - [a(n-1)]^2 ]+(1/2)[ an - a(n-1) ]
(an)^2 - [a(n-1)]^2 -2an-2a(n-1)=0
[an +a(n-1)].[an - a(n-1) -2 ]=0
an - a(n-1) -2=0
an - a1=2(n-1)
an= 2n+1
(2)
let
S = 1.2^1+2.2^2+...+n.2^n (1)
2S = 1.2^2+2.2^3+...+n.2^(n+1) (2)
(2)-(1)
S = n.2^(n+1) - ( 2+2^2+...+2^n)
= n.2^(n+1) - 2( 2^n-1)
bn=2^n
cn = an.bn
= (2n+1).2^n
=2(n.2^n) + (2^n)
Tn =c1+c2+...+cn
= 2S+ 2(2^n-1)
=2n.2^(n+1) - 4( 2^n-1) +2(2^n-1)
=2n.2^(n+1) - 2( 2^n-1)
= 2+ (4n-2).2^n

1年前

5

bachcat15 幼苗

共回答了285个问题 举报


1、当n=1时,由Sn=(1/4)an²+(1/2)an-3/4及a1=S1
得a1=(1/4)a1²+(1/2)a1-3/4
解得a1=3
当n≥2时,有an=Sn-S(n-1)
即an=[(1/4)an²+(1/2)an-3/4]-[(1/4)a²(n-1)+(1/2)a(n-1)-3/4]
化简得[an...

1年前

0
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