Question

Question about infinite series. (quickie)

Answer 1

Can you explain this statement:
For n > 1:
A(n) = S(n) - S(n-1)

Answer 2

I don't quite understand?

Answer 3

\(S(n)\) is the sum of first \(n\) terms
\(S(n-1)\) is the sum of first \(n-1\) terms

Clearly subtracting \(S(n-1)\) from \(S(n)\) gives you the \(n\)th term.

Answer 4

consider below example :
\[\begin{align}S(4) &= 1+3+5+7\\ S(3) &=1+3+5\\S(4)-S(3)&=? \end{align}\]

Answer 5

7

Answer 6

which is the \(4th\) term

Answer 7

\[\begin{align}S(4) &= 1+3+5+\color{blue}{7}\\ S(3) &=1+3+5\\S(4)-S(3)&=\color{blue}{7}\end{align}\]

Answer 8

But isn't an a sequence not the nth number?

Answer 9

you might be knowing this, but it is important to keep in mind that "sequence" and "series" are two different things.

sequence : 1, 3, 5, 7, ...

series : 1 + 3 + 5 + 7 + ...

Answer 10

sequence is just a list of numbers

series is a SUM of numbers

Answer 11

ohyes okay. I keep getting it mixed up >.<

Answer 12

\[S(n) - S(n-1) = A(n)\]

This is saying, subtracting \(n\)th PARTIAL SUM from \(n-1\)th PARTIAL SUM gives the \(n\)th TERM.

Answer 13

lets work another quick example

Answer 14

pick ur favorite sequence

Answer 15

Fibonacci

Answer 16

list down the first few terms

Answer 17

1, 1, 2, 3, 5, 8, 13...

Answer 18

I think I got it down @rational

Answer 19

Thank you for your help (:

Answer 20

sounds great! yw :)