正数数列{an}的前n项和Sn,满足2√Sn=a(n+1),猜测an的表达式并证明

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/06 10:01:02

正数数列{an}的前n项和Sn,满足2√Sn=a(n+1),猜测an的表达式并证明
请用数学归纳法证明,表示做到n=k+1时,a(k+1)=S(k+1)-Sk然后该怎么做?
我发现打错题目了- -是an + 不是a(n+1)

4Sn =an +1
By MI : an = - (-1/3)^n
n=1 , a1= 1/3
p(1) is true
Assume p(k) is true
ak= -(-1/3)^k
for n=k+1
a(k+1) = S(k+1) - Sk
= (1/4)( a(k+1) - ak)
3a(k+1) = -ak
= (-1/3)^k
a(k+1) = -(-1/3)^(k+1)
p(k+1) is true
By principle of MI, it is true for all n

已知数列（an）的前n项和为Sn,满足an+Sn=2n,证明数列(an-2)为等比数列并求出an 数列an的前n项和Sn满足：Sn=2an-3n 已知正数数列{an}的前n项和为Sn,且对于任意正整数n满足2根号Sn=an+1 求an通项数列an的前n项和为Sn=2^n-1,设bn满足bn=an+1/an,判断并证明bn 的单调性已知数列{an}的各项都为正数,a1=1,前n项和Sn满足Sn-Sn-1=根号Sn+根号Sn-1（n≥2),求数列{an 设各项都为正数的数列an 前n项和为sn 且满足Sn=1/2(an+1/an) 求证等差数列!已知数列an的各项均为正数,前n项和为Sn,且满足2Sn=a∧2n+n-4 已知数列{an}的前n项的和Sn,满足6Sn=an2+3an+2且an>0.(1)求首项a1;(2)证明{an}是数列{an}的前n项和Sn满足：Sn =2an-3n（n∈N*） 1.证明{an+3}是等比数列已知数列{a}的前n项和Sn,通项an满足Sn+an=1/2(n^2+3n-2),求通项公式an 数列An的前n项和为Sn,已知A1=1,An+1=Sn*(n+2)/n,证明数列Sn/n是等比数列已知数列｛An｝的各项均为正数,前n项和为Sn,且满足2Sn=An²+n-4 1.求证｛An｝为等差数列