已知等差数列{an}的前n项和是Sn,且a1=2,S5=30
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已知等差数列{an}的前n项和是Sn,且a1=2,S5=30
已知等差数列{an}的前n项和是Sn,且a1=2,S5=30(1)求数列{an}的通项公式 (2)若数列{bn}满足bn=2的an-1次方,求数列{bn}的前n项和是Tn (3)若数列{Cn}满足Cn=1/Sn,求数列{Cn}的前n项和是Rn
已知等差数列{an}的前n项和是Sn,且a1=2,S5=30(1)求数列{an}的通项公式 (2)若数列{bn}满足bn=2的an-1次方,求数列{bn}的前n项和是Tn (3)若数列{Cn}满足Cn=1/Sn,求数列{Cn}的前n项和是Rn
(1)
an=a1+(n-1)d= 2+(n-1)d
S5 = (2+2d)5 = 30
d=2
an = 2+(n-1)2 = 2n
(2)
bn=2^(an-1)
= 2^(2n-1)
Tn =b1+b2+...+bn
= 2(2^(2n) -1) / (4-1)
= (2/3)(2^(2n) -1)
(3)
cn =1/Sn
= 1/ [n(n+1)]
= 1/n -1/(n+1)
Rn = c1+c2+...+cn
= 1-1/(n+1)
= n/(n+1)
an=a1+(n-1)d= 2+(n-1)d
S5 = (2+2d)5 = 30
d=2
an = 2+(n-1)2 = 2n
(2)
bn=2^(an-1)
= 2^(2n-1)
Tn =b1+b2+...+bn
= 2(2^(2n) -1) / (4-1)
= (2/3)(2^(2n) -1)
(3)
cn =1/Sn
= 1/ [n(n+1)]
= 1/n -1/(n+1)
Rn = c1+c2+...+cn
= 1-1/(n+1)
= n/(n+1)
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