What is induction in math term mean?

Answer 1

It is a method of proving a statement for all values of a variable - usually for all integers. Often, the process is as follows:

Prove the statement for n = 1

Assume that the statement is true for n = k and prove that, in that case, it must be true for n = k+1.

Invoke the law of induction to assert that it is true for all [integer] values of n.