Pročitaću ostatak programa.

Both are correct, and both mean the same thing: future tense, I will read.

Serbian has two very common ways to form this future:

• Pročitaću
• Ja ću pročitati

What is happening in pročitaću is:

• infinitive: pročitati
• remove the final -i
• add the clitic ću

So:

• pročitati + ću → pročitaću

This attached form is very common in Serbian. If ću comes before the infinitive, it is written separately:

• Ja ću pročitati ostatak programa.

If the infinitive comes first, the short future form is usually written as one word:

• Pročitaću ostatak programa.

Because Serbian usually does not need the subject pronoun when the verb ending already shows who the subject is.

In pročitaću, the ending -ću tells you it is I will.

So:

• Pročitaću ostatak programa. = I will read the rest of the program.
• Ja ću pročitati ostatak programa. = same meaning, but ja adds emphasis, like I will read it.

Serbian often leaves pronouns out unless they are needed for contrast, emphasis, or clarity.

This is about aspect, which is very important in Serbian.

• čitati = imperfective
  
  • focuses on the process, repetition, or duration
  • to be reading / to read regularly
• pročitati = perfective
  
  • focuses on completing the action
  • to read through / to finish reading

In this sentence, pročitaću suggests completing the reading of the rest of it. So it is more like:

• I’ll read the rest completely / I’ll finish reading the rest

If you said Čitaću ostatak programa, that would sound more like:

• I’ll be reading the rest of the program
• or I’ll read the rest for some time

So the perfective verb fits better if the idea is finishing the remaining part.

In this verb, pro- helps create the perfective form and gives the sense of reading something through to completion.

So:

• čitati = to read
• pročitati = to read through, to finish reading

You do not always translate the prefix directly into English, but it often contributes the idea of a completed action.

Ostatak is the direct object of the verb, so it is in the accusative singular.

However, ostatak is a masculine inanimate noun, and for masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: ostatak
• accusative: ostatak

That is why the form does not change.

Because ostatak is followed by a noun in the genitive.

So the structure is:

• ostatak + genitive = the rest of ...

Examples:

• ostatak dana = the rest of the day
• ostatak knjige = the rest of the book
• ostatak programa = the rest of the program

Here:

• program = nominative singular
• programa = genitive singular

So ostatak programa literally means the rest of the program.

It is a noun phrase meaning the rest of the program.

Inside that phrase:

• ostatak = head noun
• programa = genitive dependent noun, telling you the rest of what

Then the whole phrase ostatak programa acts as the object of the verb:

• Pročitaću = I will read
• ostatak programa = the rest of the program

Yes. Program can mean several things depending on context, just like program in English.

For example, it can mean:

• a TV or radio program
• a schedule or agenda
• a software program
• a plan or platform

So ostatak programa could mean:

• the rest of the TV program
• the rest of the schedule
• the rest of the agenda
• the rest of the text of a program

The exact meaning depends on context.

No, Serbian word order is fairly flexible because case endings show grammatical relationships.

The neutral sentence is:

• Pročitaću ostatak programa.

But other orders are possible for emphasis, for example:

• Ostatak programa pročitaću.
  Emphasizes the rest of the program.
• Ja ću pročitati ostatak programa.
  Neutral with explicit subject.
• Ostatak programa ću pročitati.
  Also possible, though the placement of clitics follows special rules.

So the basic meaning stays the same, but the emphasis can change.

Because ću is a clitic, a short unstressed form that likes to attach closely to another word or appear in a special position in the sentence.

In future tense, Serbian uses forms of hteti:

• ću
• ćeš
• će
• ćemo
• ćete
• će

These are short clitic forms.

That is why you get patterns like:

• Ja ću pročitati
• Pročitaću
• On će doći
• Doći će

Clitics in Serbian follow placement rules, so they do not behave like full, freely stressed words.

Yes, in standard writing, pročitaću is written as one word.

This is the usual spelling when the infinitive comes first and combines with the future clitic:

• uradiću
• videću
• pročitaću

By contrast, when the clitic comes before the infinitive, they are written separately:

• ću pročitati
• ću uraditi
• ću videti

Roughly:

• pro-chi-TA-chu

A few helpful points:

• č sounds like ch in church
• ć is also a ch-like sound, but softer
• ću sounds roughly like chu, but with that softer ć

For many English speakers, the hardest part is hearing and producing the difference between:

• č
• ć

In everyday speech, learners are often understood even if they do not make the distinction perfectly at first, but it is good to practice it.

Yes, that is often a very good way to capture the perfective sense of pročitaću.

Because pročitati implies completion, translations like these can fit depending on context:

• I’ll read the rest of the program
• I’ll finish reading the rest of the program
• I’ll read through the rest of the program

The best English version depends on how strongly you want to show the idea of completion.

Yes.

• Pročitaću program. = I will read the program.
• Pročitaću ostatak programa. = I will read the rest of the program.

The second one implies that some part has already been read, and only the remaining part is left.

So ostatak adds the idea of what remains.

Very often, yes, when it means the rest of something.

Examples:

• ostatak vremena = the rest of the time
• ostatak novca = the rest of the money
• ostatak hrane = the rest of the food

So ostatak + genitive is a very useful pattern to remember.

Yes. That would mean I will read the rest of that program.

You can expand the noun phrase in many ways:

• ostatak programa = the rest of the program
• ostatak tog programa = the rest of that program
• ostatak novog programa = the rest of the new program

The noun after ostatak stays in the genitive, and any adjectives or determiners connected to it also match that genitive form.

The dictionary form is pročitati.

When learning Serbian verbs, you normally memorize the infinitive:

• pročitati = to read through, to finish reading

Then you build forms such as:

• pročitaću = I will read / I will finish reading
• pročitao sam = I read / I have read
• pročitaj! = read! / finish reading!

So if you want to look this verb up, search for pročitati, not pročitaću.