Question

The pattern shown is based on the sum of the cubes of consecutive positive integers. Which conjecture generalizes this pattern for all positive integers, k?

Answer 1

The sum of the cubes of consecutive positive integers can be generalized using the formula M = b^(3n) where b is the base and n is the number of times it appears in the chain.

Step-by-step explanation:

To generalize the pattern based on the sum of the cubes of consecutive positive integers, we can use the formula M = b^(3n) where b is the base and n is the number of times it appears in the chain. For example, if we want to find the sum of the cubes of the first k positive integers, we can substitute b = 1 and n = k to get M = 1^(3k) = 1. This means that the sum of the cubes of the first k positive integers is always equal to 1.