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
What is the thing inside a sum called?
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11Depending on the context, *term*, *general term*, and *summand* might all be used. – 2012-06-21
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6It's called the "summand". – 2012-06-21
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1Somewhat grotesquely, it is sometimes also called an *addend*. – 2012-06-21
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0Is there a terminologically consistent (with summand/addend/integrand) word for a factor of an infinite product (besides "factor")? – 2012-06-21
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3@deoxygerbe: Sure, multiplicand. And in "mathematics" classes, kids have to memorize these words. – 2012-06-21
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0@BrianM.Scott: *addend* was also used when I was in elementary school. – 2012-06-21
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0@robjohn: Same here; I’d forgotten about that one. – 2012-06-21
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2Its called the sumthing. – 2012-06-21
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0Do you mind if I ask how to pronounce "summand" ? Is it "sum-mand"? With emphasize on the "d" in "mand"? – 2012-06-22
2 Answers
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.
Analogously to the term "integrand," the thing inside the sum is called the "summand."