Evaluate $\sum \limits_{n=1}^\infty \frac1{L_n}$ where $L_n$ is least common multiple of $1, 2, 3,\ldots,n$
Convergence follows from $LCM(1,2,…,n)≥n(n−1)$ and $\sum_{n=2}^{\infty} \frac{1}{n(n-1)} < \infty$
Evaluate $\sum \limits_{n=1}^\infty \frac1{L_n}$ where $L_n$ is least common multiple of $1, 2, 3,\ldots,n$
Convergence follows from $LCM(1,2,…,n)≥n(n−1)$ and $\sum_{n=2}^{\infty} \frac{1}{n(n-1)} < \infty$