does .999999999999.... = 1?

My asshole friend keeps trying to tell me that .9999999... = 1

So, what's your take?

This is the only way I've had it explained to me that satisfied all doubt:

.999... = 9/10 + 9/100 + 9/1000 + ... + 9/10^n

Find the sum as n goes from 1 to infinity.

SPOILER: It equals 1.