Algebra and Series (AQA A-Level Further Maths): Quizzes

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Proof by Induction
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What is the primary purpose of proof by induction?

Prove statements for all natural numbers

What are the three essential steps in proof by induction?

Base case, inductive step, conclusion

What is the 'inductive hypothesis'?

Assuming the statement is true for n=kn = k

What must you prove in the base case?

The statement is true for n=1n = 1

In the inductive step, what must you prove?

True for n=k+1n = k + 1 using n=kn = k

In divisibility proofs, how do you use the inductive hypothesis?

Write expression as multiple of divisor

What is a common mistake in induction proofs?

Missing the base case

What must your conclusion explicitly reference?

Mathematical induction

In summation proofs, how do you write r=1k+1\sum_{r=1}^{k+1}?

r=1k+(k+1)\sum_{r=1}^{k} + (k+1)th term

What technique helps simplify algebra in summation proofs?

Look for common factors first

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