Sequences and Series
Graphs the values of a sequence
a
_{n}
and the sequence of partial sums for the series ∑
a
_{n}
.
How to use
||
Examples
||
Other Notes
How to use
Enter the formula for the
n
^{th}
term
a
_{n}
(in terms of the variable
n
) in the text input field marked "
n
^{th}
term =
". (
Example
:
a
_{n}
=1/
n
!).
Click the "
Graph
" button (this button also refreshes the graph).
Use the "+" and "-" buttons under the label marked "
n=
" to change the starting value for
n
in the sequence.
Click the "
Clear
" button to clear the text input field and set
n
to a default value.
The text input fields can accept
a wide variety of expressions
to represent functions, and the
buttons under the graph
allow various manipulations of the graph coordinates.
Examples
Harmonic
:
a
_{n}
= 1/
n
start with
n
=1
diverges
Alternating
:
a
_{n}
= (-1)
^{n}
/
n
start with
n
=1
converges
p
-Series
:
a
_{n}
= 1/
n
^{2}
start with
n
=1
converges
Factorial
:
a
_{n}
= 1/
n
!
start with
n
=0
converges
Other Notes
The graph shows the terms of the sequence {
a
_{n}
} in
red
and partial sums of the series ∑
a
_{n}
(i.e. the terms of the sequence {
S
_{n}
} where
S
_{n}
=
a
_{0}
+
a
_{1}
+...+
a
_{n}
) in
blue
on the same set of axes.