第四大题怎么做?这三个小题要不就不会收敛，要不就不会求通项？ 第1页

From the prerequisite, we know

, ,

i.e.

the characteristic equation is

,

hence we can suppose that

According to , , we get

,

thus

hence

For , and It is easy to find

Take logarithm by two sides

From

Consider the function below

,

then, owing to is monotonic as varies, we can easily obtain

Besides, there has

hence is a compression mapping on

therefore, hold only one fixed point which satisfies

thus there exists , and

Take into consideration that , we finally obtain