Series and Induction

The principle of mathematical induction involves:

Much like dominoes falling, the proof for causes the proofs for to fall into place, proving the statement to be true for all positive integers .

The following formulae can be used without proof:

Series can be manipulated in the following ways:

If the general term of a series can be written as , then:

The series won't always take this exact form; sometimes cancellations can happen two terms apart. When using the method of differences, make it clear what the cancellation pattern is.