Mario has discovered a magical mushroom that grants special powers, but only to those who can solve a tricky mathematical puzzle. To unlock the mushroom's power, one must find the sum of all positive integers less than $10^{12}$ that are either divisible by $3$ or $5$. Can you help Mario find the total sum and claim the Mushroom Power? In mathematical terms, find the sum of all positive numbers $n$ less than $10^{12}$ such that $n$ is divisible by either $3$ or $5$. Express your answer as an integer in standard notation.