数列{an}满足1/2a1+1/2^2a2+1/2^3a3……1/2^nan=2n+5. 要过程!

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数列{an}满足1/2a1+1/2^2a2+1/2^3a3……1/2^nan=2n+5. 要过程!
（1）求a1
（2）求{an}通项公式
（3）求{an}前n项和Sn

(1)
1/2a1+1/2^2a2+1/2^3a3+……+1/2^nan=2n+5 ①
当n=1时,1/2a1=2+5=7,
∴ a1=14
(2)
当n≥2时,
1/2a1+1/2^2a2+1/2^3a3+……+1/2^(n-1)a(n-1)=2(n-1)+5 ②
①-②:
1/2ⁿ*an=2,
∴an=2^(n+1)
∴{an}通项公式
an={14,n=1
{ 2^(n+1) ,(n≥2)
(3)
S1=a1=14
当n≥2时,
Sn=a1+a2+.+an
=14+[8+16+.+2^(n+1)]
=14+8[2^(n-1)-1]
=6+2^(n+2)
n=1时上式也成立
∴Sn=6+2^(n+2)

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