Question #1 - Find the corresponding sum if we add up the first n non-negative integers. This should simplify to our known formula.
Question #2 - Adapt this method to find the sum of the squares of teh first n non-negative integers. To obtain the telescoping component, use
(m + 1)^3 - m^3 = 3m^2 + 3m + 1
Question #3 - This method can be adapted to find teh sum of the kth powers of the first n non-negative integers. Apply this method to find the sum of the cubes of the first N non-negative integers and the sum of the fourth powers of the first n non-negative inters.
Question #4 - find a formula for the sum of the 10th powers of the first n non-neative integers that involved a closed form featureing an algebraic combination including n.
Question #2 - Adapt this method to find the sum of the squares of teh first n non-negative integers. To obtain the telescoping component, use
(m + 1)^3 - m^3 = 3m^2 + 3m + 1
Question #3 - This method can be adapted to find teh sum of the kth powers of the first n non-negative integers. Apply this method to find the sum of the cubes of the first N non-negative integers and the sum of the fourth powers of the first n non-negative inters.
Question #4 - find a formula for the sum of the 10th powers of the first n non-neative integers that involved a closed form featureing an algebraic combination including n.