Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 50 centuries, what is the total (in hours) of the daily increases in time (that is, the sum of the gain on the first day, the gain on the second day, etc.)?
Awfully worded question
So, in one century the length of an Earth day increased by 1.0ms. Therefore in 36500 days the length increases by 1.0ms. But this is where I think we need a bit more info. If the increases are following some kind of sequence then we could use the formula for the sum of an arithmetic/geometric sequence, but we don't know that.
Im gonna have an absolute stab in the dark and say 0.05 seconds, but surely it's not that easy haha.
Sorry I can't be more helpful.