To simplify the expression, we can combine like terms:

s = 1 - 11/6 + 19/12 - 29/20 + 41/30 - 55/42 + 71/56 - 89/72 + 109/90

First, let's find a common denominator for all the fractions. The least common multiple (LCM) of the denominators 6, 12, 20, 30, 42, 56, 72, and 90 is 2520.

Now, we can rewrite each fraction with the common denominator:

s = (1 * 420) / 2520 - (11/6 * 420) / 2520 + (19/12 * 420) / 2520 - (29/20 * 420) / 2520 + (41/30 * 420) / 2520 - (55/42 * 420) / 2520 + (71/56 * 420) / 2520 - (89/72 * 420) / 2520 + (109/90 * 420) / 2520

Simplifying each fraction:

s = 420/2520 - 4620/2520 + 7980/2520 - 12180/2520 + 14340/2520 - 11550/2520 + 10710/2520 - 10395/2520 + 16380/2520

Now, let's add or subtract the numerators:

s = (420 - 4620 + 7980 - 12180 + 14340 - 11550 + 10710 - 10395 + 16380) / 2520

Simplifying the numerator:

s = (-1005) / 2520

Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 15:

s = (-1005/15) / (2520/15)
s = -67/168

Therefore, the simplified value of s is -67/168.