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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.
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Base Case of Mathematical Induction
What is it?
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.
In simple words
- 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.
Important terms
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.
What you should learn
- 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.
Examples
- n=1 arithmetic
- Both sides numbers
- Do not skip
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.
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.
Recommended for Class 11
Full school-level explanation
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.
Understand the idea, then apply it:
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.
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.
Remember
- check the first n
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.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a base case of mathematical induction question
How it works
- 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.
Remember
- check the first n
- base then step
- assume P(k), prove P(k+1)
- need the first domino
- check the first n
- focused answer
- accurate support
- check the first n
Deeper understanding
Go beyond memorising Base Case of Mathematical Induction. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- check the first n
- base then step
- assume P(k), prove P(k+1)
- need the first domino
- 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: Usually n=1: plug in and check a number identity.
You must do both base and step. The step alone does not start the chain.
For long answers on Base Case of Mathematical Induction: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- check the first n
- base then step
- assume P(k), prove P(k+1)
- need the first domino
Important formulas
- check the first n
- base then step
- assume P(k), prove P(k+1)
Common exam traps
- You must do both base and step. The step alone does not start the chain.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
You must do both base and step. The step alone does not start the chain.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
You must do both base and step. The step alone does not start the chain.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
check the first n
base then step
assume P(k), prove P(k+1)
need the first domino
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.
- 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.
- Example
- n=1 arithmetic
- Critical warning
- You must do both base and step. The step alone does not start the chain.
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Exam Practice
Define
Q1. Define Base Case of Mathematical Induction.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Base Case of Mathematical Induction and say why it fits.
Mistake
Q4. State one common mistake students make about Base Case of Mathematical Induction.
Exam note
Q5. Write a short exam note on Base Case of Mathematical Induction: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.