As you have mentioned it may be your typing mistake that you have written
package javax.Servlte.Http.*; change it to the package javax.servlet.http.*;
If you are typing correctly then it may be that you have not set the classpath of your java-servlet-api.jar in the environment variables.
Visit the following link to know about setting classpath and environment variables.http://www.roseindia.net/servlets/HowToRunAServlet.shtml