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9231 FP1 · Notes & worked examples

Proof by induction for divisibility · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Induction and divisibility — objective 1

Maths4U Original · Short practice

Work with the integer powers \(5^n-3^n\).

Find \(\displaystyle \frac{5^{3}- 3^{3}}{2}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Induction and divisibility — objective 1

Maths4U Original · Short practice

Work with the integer powers \(7^n-4^n\).

Find \(\displaystyle \frac{7^{4}- 4^{4}}{3}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Induction and divisibility — objective 2

Maths4U Original · Short practice

Work with the integer powers \(7^n-4^n\).

Find the difference at \(\displaystyle n=1\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Induction and divisibility — objective 2

Maths4U Original · Short practice

Work with the integer powers \(9^n-5^n\).

Find the difference at \(\displaystyle n=1\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Induction and divisibility — objective 3

Maths4U Original · Short practice

Work with the integer powers \(9^n-5^n\).

Find the quotient at \(\displaystyle n=6\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Induction and divisibility — objective 3

Maths4U Original · Short practice

Work with the integer powers \(4^n-2^n\).

Find the quotient at \(\displaystyle n=4\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Induction and divisibility — objective 4

Maths4U Original · Short practice

Work with the integer powers \(4^n-2^n\).

Find the integer remainder term \(\displaystyle 2^3\) in the successor quotient relation.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Induction and divisibility — objective 4

Maths4U Original · Short practice

Work with the integer powers \(6^n-3^n\).

Find the integer remainder term \(\displaystyle 3^4\) in the successor quotient relation.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Try written exam-style problems →