设数列{an}为等差数列,前n项和为Sn,已知a2=2,S5=15.(1)求{an}的通项公式.(2)若bn=an/2的n次方,求数列{bn}的前n项和Tn

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设数列{an}为等差数列,前n项和为Sn,已知a2=2,S5=15.(1)求{an}的通项公式.(2)若bn=an/2的n次方,求数列{bn}的前n项和Tn
设数列{an}为等差数列,前n项和为Sn,已知a2=2,S5=15.(1)求{an}的通项公式.(2)若bn=an/2的n次方,求数列{bn}的前n项和Tn

设数列{an}为等差数列,前n项和为Sn,已知a2=2,S5=15.(1)求{an}的通项公式.(2)若bn=an/2的n次方,求数列{bn}的前n项和Tn
(1)由a1+d=2和5a1+10d=15解得a1=1,d=1,∴an=n
(2)由bn=n/2^n得,Tn=½+2/2^2+3/2^3+.+n/2^n,
Tn/2=1/2^2+2/2^3+3/2^4+.+(n-1)/2^n+n/2^(n+1)
两式相减得Tn/2=1/2+1/2^2+1/2^3+.+1/2^n-n/2^(n+1)=(1-1/2^n)-n/2^(n+1)=1-(2+n)/2^(n+1)

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