提问数列的题目.数列{an},an>0,Sn=(1/2)*(an+(1/an)),求an.
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提问数列的题目.
数列{an},an>0,Sn=(1/2)*(an+(1/an)),求an.
数列{an},an>0,Sn=(1/2)*(an+(1/an)),求an.
an>0,Sn=(1/2)*(an+(1/an)),
a1=0.5(a1+1/a1)
a1=1
2Sn*An=An ^2 +1
2Sn*(Sn-S(n-1))=(Sn-S(n-1) )^2 +1
2Sn ^2 -2Sn*S(n-1)=Sn^2 -2Sn*S(n-1)+S(n-1)^2 +1
Sn^2 -S(n-1)^2 =1
所以Sn^2为等差数列 根据题目中式子:2S1=A1 +(1/A1) => S1=A1=1
Sn^2=1+n-1=n
An=Sn -S(n-1) =根号n-根号(n-1)
a1=0.5(a1+1/a1)
a1=1
2Sn*An=An ^2 +1
2Sn*(Sn-S(n-1))=(Sn-S(n-1) )^2 +1
2Sn ^2 -2Sn*S(n-1)=Sn^2 -2Sn*S(n-1)+S(n-1)^2 +1
Sn^2 -S(n-1)^2 =1
所以Sn^2为等差数列 根据题目中式子:2S1=A1 +(1/A1) => S1=A1=1
Sn^2=1+n-1=n
An=Sn -S(n-1) =根号n-根号(n-1)
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