Collatz sequences originate from dividing an even number by two until an odd number is obtained, followed by multiplication by three and an increment of one to yield an even number. The Collatz conjecture posits that the repeated application of this process inevitably results in the number one. The Collatz conjecture holds true for every number tested, but no general method has been found to prove that it is true for all positive integers. We introduce a new methodology: the binary series. In conjunction with mathematical induction, this new methodology provides a more general method of testing positive integers for properties that cannot be established by induction alone. We partition the positive integers into distinct subsets. The binary series allows us to use geometric series that sum to one (100%) to show that all natural numbers satisfy the Collatz conjecture. This new methodology eliminates the need to test every integer and provides a general method of proof for the Collatz conjecture.