COPYRIGHT NOTICE
Copyright 2007 Samuel Dagan
dagan@post.tau.ac.il
/general/copyright.xhtml
Convergence of a sequence
The crossing of a(n)=1 horizontal line with n=1 vertical - at
user=0,0)
The origin of the figure is at (0,0)
© Samuel
Dagan
Convergence of a sequence
an
1
1+ε
1−ε
n=
""
""
""
""
""
""
""
""
""
""
""
""
""
""
""
""
""
""
""
""
ε = 1
twice
half
ε=1
ε
control
left
right
reset
n
control
an
=
n² + 2n − 3
n² − 3n+7
for n>N: |
an − A
| < ε
The terms of the sequence
defined by the formula of an
framed in black (above on the right)
are displayed by blue
dots along the vertical axis. The sequence converges to A = 1 .
This window opens with ε=1
and its value is going to be displayed at each time on
the top right.
For ε = 1
and n>N = 1 , the
purple framed requirement holds (above on the right).
Clicking the "half" button makes
ε = 0.5 ,
which corresponds to N = 10 .
Clicking the "left" button moves the
horizontal scale to the left by one n unit .
After clicking about 10 times
and making ε = 0.25 , one obtains N = 20 .
With the use of these and the
other buttons, one can obtain N = 40 for
ε = 0.125 etc. Enjoy!
restart
Use the zoom of your system
to resize this window
Use the mouse to pan and
to resize the graphics
ani-
mate
pause
resume
fast
slow
pause
fast
slow
next
next
end