Proving Divisibility by Induction | Mr Mathematics

Proving divisibility by induction often poses challenges, particularly with common mistakes such as misunderstanding the induction step or incorrect algebraic manipulation. Members of my site can access the full lesson, which includes additional examples and a student handout, perfect for reinforcing classroom learning.

The first question introduces proof by induction with a simple quadratic expression, ensuring students grasp the foundational process. By the second question, where the expression involves powers, students are challenged to apply the rules of indices effectively and substitute the exponential terms with f(k). The third question combines an exponential and linear term, requiring a deeper understanding of how to manipulate functions within the induction framework.

For a comprehensive learning experience, remember that Mr. Mathematics membership provides full access to these resources and more, enabling you to support your students in mastering difficult topics like divisibility by induction.

Keywords: Proving divisibility by induction, A-Level Further Mathematics, proof by induction, divisibility, curriculum specification.

About Me:
I’m Jonathan Robinson, Head of Maths in the South East of England with over 20 years of teaching experience. My goal is to help teachers worldwide engage and inspire their students with my lessons.

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