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We are learning about it and my teacher didn't explain why either Sigma nor Pi were used.

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It's phonetic - $\Sigma$ stands for "sum" and $\Pi$ stands for "product.

Noah Schweber
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$\pi$ is a capital letter from the Greek alphabet called “Pi", it corresponds to “P” in our alphabet. So, "p"roduct notation is derived from the symbol of "Pi", $\pi$. A similar reasoning holds for the summation symbol, sigma.