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No, a person cannot improve his/her credit score by buying it for money. There is no such thing as good credit score for sale. All you can do is get your own credit report and find the issues that are deterrent to good credit health. Once you have identified the negative issues, take action to clear them.
Negative issues such as settlement, written off accounts, defaults, late payments etc could hurt your credit score badly. Moreover, credit score is computed based on various parameters such as credit history, on-time payments, credit mix, credit enquiries, credit utilisation ratio etc. By keeping tabs on these parameters, you will be able to obtain a good credit score ultimately.