a^n=(1+(a-1))^n
=n + n·(a-1) + n(n-1)/2·(a-1)² + .
=n·[1 + (a-1) + (n-1)/2·(a-1)² + .]
n/a^n
=1/[1 + (a-1) + (n-1)/2·(a-1)² + .]
≤1/[(n-1)/2·(a-1)²]
=2/[(n-1)·(a-1)²]
对任意的ε>0
取N=不小于2/(ε·(a-1)²) + 1的整数
怎么用极限严格定义求数列n\(a^n)的极限.
a^n=(1+(a-1))^n
=n + n·(a-1) + n(n-1)/2·(a-1)² + .
=n·[1 + (a-1) + (n-1)/2·(a-1)² + .]
n/a^n
=1/[1 + (a-1) + (n-1)/2·(a-1)² + .]
≤1/[(n-1)/2·(a-1)²]
=2/[(n-1)·(a-1)²]
对任意的ε>0
取N=不小于2/(ε·(a-1)²) + 1的整数