The sum of the series 1+1/2+1/4+1/8+...+1/128 can be found using the formula for a geometric series:

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

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 1, r = 1/2, and n = 7 (since there are 7 terms in the series).

Plugging in these values, we get:

S = 1(1 - (1/2)^7)/(1 - 1/2)
S = 1(1 - 1/128)/(1/2)
S = 1(127/128)/(1/2)
S = 127/64

Therefore, the sum of the series 1+1/2+1/4+1/8+...+1/128 is 127/64.