If you really need something to convince parents, but you don't know how to begin, try to understand what prevents them to give their consent immediately. No need to fight, and just figure out their response to your request.
In order for your request not looked childish Caprice, which is not worth paying attention to, think about what you kind of thing, or trip is so necessary.
I can say that your friends have a similar laptop, mobile phone, or their parents go on a camping trip, and you will have to stay home. To give examples can only after you will be able to explain why this thing is important to you.
If you ever promise to your parents in return for the purchase, trip, you should keep it, otherwise next time you won't believe and deem not responsible enough and an adult to trust you. For example, you promised that if you buy a laptop, you will finish study this year on "perfectly". But you are too lazy to learn the lessons, want to play new exciting games, walk on the street. You break the promise, and the result is parents can simply select the computer you have, while your GPA will not rise up to the promised standard.
Never quarrel with parents, if something they are asking for. If you can't buy an expensive thing because of lack of money, it is not necessary to scream, fall to the floor in hysterics, blaming parents in poverty – and so they are doing everything they can to make you dressed and fed. Try to cancel part of your pocket money to pay part of the amount for your desired item. This once again proves to parents that you are old enough and know the value of money.
If you need to go somewhere, do not hesitate to call for help of his friends, whom your parents trust. If your friends vouch for you, it is possible to permit you have started by the event.