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You know how the "thing" inside an integral, we call that an integrand. Does any know what the $a_n$ in a typical $\sum a_n$ is called? Or do we only have names if it is an infinite series? I could've sworn there is a name or there really should be a name

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    Do$ $you mind if I ask how to pronounce "summand" ? Is it "sum-mand"? With emphasize on the "d" in "mand"?2012-06-22

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Any element of a sum is called a summand. For example: $2$, $4$ and $6$ are summands in $2+4+6 = 12$, and in $\sum a_i$ each of the $a_i$ are summands, that is, $a_1$, $a_2$, $a_3$, etc. are summands.

However, in $\sum a_i$, we can also call $a_i$ the general term of the sequence $(a_n)$, but that's specific to sequences and series, because it makes a reference to the role of $a_i$ in the sequence, unlike the name summand, which only refers to the fact that a quantity is being summed (actually, that's the etymology of the word: sum, with a gerund ending), or is part of a sum.

The name term applies to both concepts, and probably to more general settings too.

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Analogously to the term "integrand," the thing inside the sum is called the "summand."