MathematicsChapter 7: Mathematical Induction and Binomial Theorem
Base Case of Mathematical Induction
Usually n=1: plug in and check a number identity.
Learning objectives
- State the rule or meaning of base case of mathematical induction in easy words.
- Apply base case of mathematical induction in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Usually n=1: plug in and check a number identity. If the claim starts at n=2, start there. A failed base kills the proof even if the step looks pretty.
Where / symbols
- BASE CASE OF MATHEMATICAL INDUCTION
- Usually n=1: plug in and check a number identity. If the claim starts at n=2, start there. A failed base kills the proof even if the step looks pretty.
- BASE
- Usually n=1: plug in and check a number identity.
Overview
Understand the idea, then apply it:
Main Idea
Usually n=1: plug in and check a number identity. If the claim starts at n=2, start there. A failed base kills the proof even if the step looks pretty.
Examples n=1 arithmetic · Both sides numbers · Do not skip
Exam Use
Write the rule first: Usually n=1: plug in and check a number identity. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — BASE CASE OF MATHEMATICAL INDUCTION
Usually n=1: plug in and check a number identity. If the claim starts at n=2, start there. A failed base kills the proof even if the step looks pretty.
WHY — Why it matters
This rule is a separate learning unit inside principle of mathematical induction. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Usually n=1: plug in and check a number identity. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a base case of mathematical induction question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
You must do both base and step. The step alone does not start the chain.
Key points
- check the first n
- base then step
- assume P(k), prove P(k+1)
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Base Case of Mathematical Induction
Sticky Notes · Quick Revision
Core Idea
- Usually n=1: plug in and check a number identity.
What to Know
- Usually n=1: plug in and check a number identity. If the claim starts at n=2, start there. A failed base kills the proof even if the step looks pretty.
Example or Evidence
- n=1 arithmetic
- Both sides numbers
- Do not skip
How to Answer
- Write the rule first: Usually n=1: plug in and check a number identity. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- You must do both base and step. The step alone does not start the chain.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Usually n=1: plug in and check a number identity.
- n=1 arithmetic
- Both sides numbers
- State the rule, show the working, and check the answer.
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