1. Use Python write a function sum_to(n) in two different ways that returns the sum of all integer numbers up to and including n. So sum_to(10) would return the value 55: a) Use the equation (n * (n + 1)) / 2 b) Use the recursion method.

2. Use Python write a program that creates a list of 100 random integers between 0 and 1000 (use iteration, append, and the random module). a) Write a function called average_value that will take the list as a parameter and return the average. b) Write function max_value that will take a list of 100 random integers between 0 and 1000 and return the maximum value. (Note: there is a built-in function named max but we do not want to use it in this function.)

3. Dictionaries provide an elegant way to generate a frequency table: Use Python write a program that displays a dictionary that includes the letters and their frequencies in the string "Newtownmountkennedy.