Proof by induction for divisibility: check 1
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: review variant 1
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: check 2
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: review variant 2
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: check 3
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: review variant 3
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: check 4
Difficulty: ★★☆Info
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.
Proof by induction for divisibility: review variant 4
Difficulty: ★★☆Info
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.