series

If the sum of the first 20 consecutive positive odd numbers is divided by 20^2, the result is

$a + a + a + \dots + a = a^2b$ (n times) and $b + b + b + \dots + b = ab^2$ (m times), where a, b, n and m are natural numbers. What is the value of $(m + m + m + \dots + m)$ (n ti...

Consider a sequence of numbers $a_1, a_2, a_3, \dots, a_n$ where $a_n = \frac{1}{n} - \frac{1}{n+2}$, for each integer $n > 0$. What is the sum of the first 50 terms?