Tính nhanh: A= 3^ 2019 +1 1 + 3 + 3 ^ 2 + 3 ^ 3 +...+3^ 2017 +3^ 2018 -3^ 2019

To simplify the given expression, let's break it down step by step.

First, let's rewrite the expression for clarity:

\[ A = 3^{2019} + 1 + 3 + 3^2 + 3^3 + \ldots + 3^{2017} + 3^{2018} - 3^{2019} \]

Notice that \( 3^{2019} \) appears both as a positive term and as a negative term, so they cancel each other out:

\[ 3^{2019} - 3^{2019} = 0 \]

This simplifies the expression to:

\[ A = 1 + 3 + 3^2 + 3^3 + \ldots + 3^{2017} + 3^{2018} \]

Now, we recognize that this is a geometric series with the first term \( a = 1 \) and the common ratio \( r = 3 \). The number of terms in this series is \( 2019 \) (from \( 3^0 \) to \( 3^{2018} \)).

The sum \( S \) of a geometric series can be calculated using the formula:

\[ S = a \frac{r^n - 1}{r - 1} \]

where \( a \) is the first term, \( r \) is the common ratio, and \( n \) is the number of terms.

In this case:

- \( a = 1 \)
- \( r = 3 \)
- \( n = 2019 \)

Plugging these values into the formula, we get:

\[ S = 1 \cdot \frac{3^{2019} - 1}{3 - 1} \]
\[ S = \frac{3^{2019} - 1}{2} \]

Therefore, the simplified form of the given expression \( A \) is:

\[ A = \frac{3^{2019} - 1}{2} \]