In the first instance of "service", the sentence has not defined it as (a=one) service, so it is not countable. In the second sentence the bank defines it as "a new service", defined as more than one service already exists.= countable. Sentence one is generic, sentence two is specific as far as being countable is concerned. So, there are nuances that are learned after practice. The easy answer is, can you count it?

As others have said, when it's countable it's more specific, when it's uncountable it's more general. The main difference between using countable or uncountable is the way you think about the information. "The department is capable of providing specialized rescue service." Because "service" is uncountable here, it refers to the service in a general sense. In this sentence we can think of "service" as a term that encompasses every different thing that can be done by the department when they do a specialized rescue. Maybe in different situations they do different things, so the general "service" refers to all those possibilities. If we make it countable... "The department is capable of providing a specialized rescue service." This suggests that the department offers many types of service, but we're specifically talking about the service of specialized rescue. The sense I get from this sentence is that the specialized rescue service is one option among others. Let's look at your other example. "The bank is offering a new service that will allow patrons to examine personal transactions listed in a consolidated weekly statement." "Service" is countable here because it specifies one type of service, namely the ability to examine personal transactions in a weekly statement. The bank may offer other types of service too, but in this sentence we're only talking about weekly statements. If we make it non-countable... "The bank is offering new service that will allow patrons to examine personal transactions listed in a consolidated weekly statement." This sentence sounds awkward to me. It could be correct if the weekly transaction statement is only one part of the new service that the bank offers. However, because the sentence discusses a very specific description of the new service, making it countable sounds more logical. I hope that makes sense. The difference is subtle, so it's hard to explain well.

think about it, can u count it or no, and you will find the answer :)

The word "service" is both countable and uncountable, and its usage depends on the context in which it is used. Sometimes you will find it as "services" refering to more than one service. Hi Tay, my name is Uri Quintal. I am an ESL and Spanish teacher graduated from the Arizona State University in Phoenix, Az. I offer some basic lessons for non-native Spanish and English speakers in order to help students not only to speak another language but to think and dream in another language for a very cheap price. Please feel free to contact me if you are interested. Have a nice day! :)