To find the value of X, we need to find the sum of the arithmetic series 1+2+3+4+...+X.

The sum of an arithmetic series can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, the first term (a) is 1, and we need to find the value of X when the sum (Sn) is 3240.

So, we have the equation: 3240 = (X/2)(1 + X)

Expanding the equation, we get: 3240 = (X^2 + X)/2

Multiplying both sides of the equation by 2, we get: 6480 = X^2 + X

Rearranging the equation, we get: X^2 + X - 6480 = 0

Now, we can solve this quadratic equation to find the value of X.

Using factoring or the quadratic formula, we find that X = 80 or X = -81.

Since X represents the number of terms in the series, it cannot be negative. Therefore, the value of X is 80.