a. Prove that for all n E N, 1+2+3+...+ n = n(n + 1) 2 b. Suppose you have a book whose pages are numbered from 1 to 100. Use the formula in part a to find the sum of all of the page numbers in the book. c. Suppose that someone has taken the book from part b and torn out the sheet of paper that had page 53 on one side and page 54 on the other side. What is the sum of all of the remaining page numbers in the book?