- #1
Vishera
- 72
- 1
It's been a while since I've dealt with sequences and series. Here is my explanation of sequences and series and let me know if I am right or wrong.
A sequence is just a list of numbers. By convention, we use the letter ##a## for sequences and they are written in a form like so: ##a_1,a_2,a_3,a_4,...##
A sequence can be finite or infinite.
1,2,3,4 is a finite sequence. 1,2,3,4,... is an infinite sequence.
An arithmetic sequence, for some constant d: ##a_n=a_0+dn##
A geometric sequence, for some constant r: ##a_{ n }=a_{ 0 }r^{ n }##
A series is the sum of the terms of a sequence. By convention, is there a letter for series? I can't remember. Let us use the letter S in the meantime. Series are written like so: ##S_1,S_2,S_3,S_4,...##
Let Sn be the series of the finite sequence mentioned earlier. S1=1. S2=3. S3=6. S4=10.
Let Sn be the series of the infinite sequence mentioned earlier. S=∞
I feel like I'm doing something wrong. Can anyone briefly mention which parts are wrong?
A sequence is just a list of numbers. By convention, we use the letter ##a## for sequences and they are written in a form like so: ##a_1,a_2,a_3,a_4,...##
A sequence can be finite or infinite.
1,2,3,4 is a finite sequence. 1,2,3,4,... is an infinite sequence.
An arithmetic sequence, for some constant d: ##a_n=a_0+dn##
A geometric sequence, for some constant r: ##a_{ n }=a_{ 0 }r^{ n }##
A series is the sum of the terms of a sequence. By convention, is there a letter for series? I can't remember. Let us use the letter S in the meantime. Series are written like so: ##S_1,S_2,S_3,S_4,...##
Let Sn be the series of the finite sequence mentioned earlier. S1=1. S2=3. S3=6. S4=10.
Let Sn be the series of the infinite sequence mentioned earlier. S=∞
I feel like I'm doing something wrong. Can anyone briefly mention which parts are wrong?