Warm up problem 7: telescoping series easy-medium

Finalized my solution. To understand this solution, it is helpful if you read this inorder to understand the Heaviside function. However, if you have trouble understanding this article or my solution, feel free to ask any question you may have. I'd be more than happy to answer it as telescoping functions are great but can get quite tricky.

By Heaviside function. $\dfrac{1}{a(a+2)}=\dfrac{1}{2}\left(\dfrac{1}{a}-\dfrac{1}{a+2}\right)$

$\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...\dfrac{1}{483}$

$\dfrac{1}{1 \times 3}+\dfrac{1}{3 \times 5}+\dfrac{1}{5 \times 7}+...\dfrac{1}{21\times 23}$

$\dfrac{1}{2}\left( \left( 1-\dfrac{1}{3} \right)+\left(\dfrac{1}{3}-\dfrac{1}{5}\right)+\left(\dfrac{1}{5}-\dfrac{1}{7}\right)...+\left(\dfrac{1}{21}-\dfrac{1}{23}\right) \right)$

$\dfrac{1}{2}\left( 1-\dfrac{1}{23} \right)$

$\dfrac{11}{23}$

$\boxed{11+23=34}$