=∑(X)^(3n)

Next, we cannot generalize. Discuss the value of X. Different values of X will lead to different results. ..

( 1)- 1 & lt； X< in 1:

This is a geometric series whose absolute ratio is less than 1, and the sum of the first n terms has a limit:

∑(X)^(3n)=(X^3)/( 1-X^3)

(2)X=- 1

This series is:-1, 1,-1, 1. . .

So there is no limit.

(3)X= 1

This series is: 1, 1, 1, 1,. .

The first n terms and regions are infinite, and the limit does not exist.

(4)|X| > 1

The absolute value of geometric progression's common ratio is greater than 1, so the series diverges and the limit does not exist.