To find the sum of the series 1+3+9+27+...+729, we can observe that each term is obtained by multiplying the previous term by 3. This is a geometric series with a common ratio of 3.

The formula to find the sum of a geometric series is given by:

S = a * (r^n - 1) / (r - 1)

Where:
S = sum of the series
a = first term
r = common ratio
n = number of terms

In this case, the first term (a) is 1, the common ratio (r) is 3, and we need to find the sum of 6 terms (n = 6).

Plugging these values into the formula, we get:

S = 1 * (3^6 - 1) / (3 - 1)
S = 1 * (729 - 1) / 2
S = 1 * 728 / 2
S = 364

Therefore, the sum of the series 1+3+9+27+...+729 is 364.