Notice the short clipped sentences - even fragments - that Gene uses at the end of the chapter. Why is this effective?What does this convey to the...

You unfortunately don't specify the end of which chapter you are referring to. There are two endings however that could be applicable to what you are stating. The first is the end of Chapter 2 where Gene dwells on how Finny saved him from falling off the tree (obviously ironic as Gene goes on to make Finny fall from the same tree):

It was only after dinner, when I was on my way alone to the library, that the full danger I had burshed on teh limb shook me again. If Finny hadn't come up right behind me... if he hadn't been there... I could have fallen on the bank and broken my back! If I had fallen awkwardly enough I could have been killed. Finny had practically saved my life.

Although not particularly short, the sentences, especially the fragments, reflect Gene's horror at what could have happened had Finny not been there to save him. The way that these fragments only begin and do not end augment the terror of these thoughts - literally, Gene stops himself from completing the sentences as the thought of what could have happened is to shocking to contemplate.

The other chapter comes after Gene has gone to see Leper in his home after he returned from the army:

I left Leper telling his story into the wind. He might tell it forever, I didn't care. I didn't want to hear any more of it. I had already heard too much. What did he mean by telling me a story like that! I didn't want to hear any more of it. Not now or ever. I didn't care because it had nothing to do with me. And I didn't want to hear any more of it. Ever.

Here, the short, clipped sentences reflect Gene's mood of anger and rage at Leper for being forced to confront the realities of the war. It reflects how he is trying to limit his vision and ignore central truths about war, humanity, and truths about Gene himself that he does not want to face and is determined to repress. Leper and his experiences "opens the lid" on these feelings that Gene is obviously supressing, and thus the short sentences demonstrate the determination and stubborness Gene adopts in ignoring these truths and continuing to live in his illusory world.