The idea of this problem is not difficult to find, and the key lies in the handling of some details.

There are two main ideas:

1.

Builder t (n) = 10 f (n) * (4/5) g (n)

Solve the equation T(n) > t (n-1) t (n) > t (n+1) to find the extreme value of t (n) and compare it with 4.

2.

Mathematical induction.

One thing to pay attention to is that when you start, you must list it to 4. This is correct when it extends from n to n+ 1

Of course, there are other ways to solve this problem, but the above two methods are common, and others, such as scaling, are too strong, so I won't introduce them here.