1.
an=1+(√80-√79)/(n-√80)
当n<=8,an为减函数,a1>a2>a3...>a8
当n>=9,an为减函数,a9>a10>a11...>a50
a1=(1-√79)/(1-√80)
a9=(9-√79)/(9-√80)
a1-a9=8(√80-√79)/[(1-√80)(9-√80)]<0
a1<a9,a9最大
a8=(8-√79)/(8-√80)
a50=(50-√79)/(50-√80)
a8-a50=42(√80-√79)/[(8-√80)(50-√80)]<0
a8<a50,a8最小
2.图中135标的位置不正确
设第n层数高度为an
a1=1,a3=1/4,a5=1/16,....an=1/4^(k-1),(n=2k-1,k∈N)
a2=√2/4,a4=√2/16,...an=√2/4^k,(n=2k,k∈N)
n层树的高度
S1=a1=1
n>=2
当n为偶数:
Sn=(√2+4)(4^k-1)/(3*4^k),(n=2k,k∈N)
当n为奇数:
Sn=(√2+4)(4^k-1)/(3*4^k)+1/4^k,(n=2k+1,k∈N)
