Due: Friday, October 13, at the beginning of class.
Show your work for each problem. Don't guess. You should be able to convince a skeptical person that your answer is correct.
Give a formula for the sum for k = 1 to n of 3k+1, where n ≥ 1.
Give a formula for the sum for k = 1 to n of 5k+2, where n ≥ 1.
What is the value of the sum for k = 0 to 200 of 2(4k)? Do not try to write it out as a number. Express it using powers of 4, such as 4200.
What is the sum for k = 0 to infinity of 3/(5k)? Give the result as a number.
Using mathematical induction, prove that the sum from k = 1 to n of 1/(k(k+1)) is 1 - 1/(n+1) for all n ≥ 1.
Using mathematical induction, prove that The sum from k = 1 to n of k(k+1) is equal to (n(n+1)(n+2))/3 for all n ≥ 1.