(1)等差数列{1/an}满足a1=1,公差d=2,求a1a2+a2a3+...+ana(a+1)的和
(2)比较x^6+1与x^4+x^2的大小
人气:383 ℃ 时间:2020-03-31 23:23:51
解答
1/an=1+2(n-1)=2n-1
an=1/(2n-1)
ana(a+1)=0.5(1(/2n-1)-1/(2n+1))
tn=0.5(1-1/3+1/3-1/5---+1(/2n-1)-1/(2n+1))
=0.5(1-1/(2n+1))
=n/(2n+1)
x^6+1与x^4+x^2的大小
设f(x)=x^6+1-(x^4+x^2)
=(x^4-1)(x^2-1)
=(x^2+1)*(x^2-1)^2
x^2+1》1
当x=+-1时候,相等(这里还可以由虚数解略;其余前者大
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