More examples
Problem 9: Prove that \(24|(5^{2n}-1)\) for all integers \(n\ge 0\).
Problem 21: Prove that \[ \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2^{n}-1}+\frac{1}{2^{n}}\ge 1+n/2 \] and conclude that the harmonic series diverges.
Problem 9: Prove that \(24|(5^{2n}-1)\) for all integers \(n\ge 0\).
Problem 21: Prove that \[ \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2^{n}-1}+\frac{1}{2^{n}}\ge 1+n/2 \] and conclude that the harmonic series diverges.