What does this notation mean $\{a_k\}_{k=i}^n$?
I saw it in sites talking about sequences but there was no explanation of what it meant.
E: I reviewed the other post, this is not a duplicate, and the chosen answer described what I asked.
Asked
Active
Viewed 513 times
2
-
possible duplicate of Notation for sequences – Jun 12 '15 at 15:28
-
The other question asks what notation to write for infinite sequences; this question concerns how to read a notation which (it happens) is for finite sequences (or subsequences). This does not seem a duplicate to me. – David K Jun 13 '15 at 01:28
2 Answers
3
${\{a_k\}}_{k=i}^n$ means the list of terms in the sequence $a_k$, ranging from $k=i$ to $k=n$; i.e.:
$$a_i,a_{i+1},a_{i+2},...,a_n$$
Ant
- 2,407
-
-
-
I would assume ${a_k}{k=i}^n$ was the set ${a_i, \dots a_n}$, but $(a_k){k=i}^n$ was the list $(a_i, \dots, a_n)$. – Thomas Ahle Jun 01 '19 at 15:23
2
It means the following collection of objects: $$\{a_k\}_{k=i}^n=\left \{ a_i,a_{i+1},a_{i+2},\dots,a_n \right \}$$
- For example, if $i=1$ and $n=5$, we would have: $$\{a_k\}_{k=1}^5=\left \{ a_1,a_{2},a_{3},a_{4},a_5 \right \}$$
Meshal
- 779