(3^(n+1)+5^(n+1))/(3^n+5^n)当n趋向无穷大时的极限是多少?怎么算的,
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(3^(n+1)+5^(n+1))/(3^n+5^n)当n趋向无穷大时的极限是多少?怎么算的,
![(3^(n+1)+5^(n+1))/(3^n+5^n)当n趋向无穷大时的极限是多少?怎么算的,](/uploads/image/z/15761215-55-5.jpg?t=%EF%BC%883%5E%EF%BC%88n%2B1%EF%BC%89%2B5%5E%EF%BC%88n%2B1%EF%BC%89%EF%BC%89%2F%EF%BC%883%5En%2B5%5En%EF%BC%89%E5%BD%93n%E8%B6%8B%E5%90%91%E6%97%A0%E7%A9%B7%E5%A4%A7%E6%97%B6%E7%9A%84%E6%9E%81%E9%99%90%E6%98%AF%E5%A4%9A%E5%B0%91%3F%E6%80%8E%E4%B9%88%E7%AE%97%E7%9A%84%2C)
分子分母同除以5^n得:lim(3^(n+1)+5^(n+1))/(3^n+5^n)
=lin(3(3/5)^n+5)/((3/5)^n+1)=5
(3/5)^n趋于0
=lin(3(3/5)^n+5)/((3/5)^n+1)=5
(3/5)^n趋于0
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