Hi, I have the following exercise... I have solved the first question, but I don't know about the second question. Thanks for whatever help you have give me!
Since early electronic computers had no automatic division, it was necessary to accomplish this by a process of calculating reciprocals using only addition, subtraction and multiplication.
1) Show that the Newton-Raphson method iteration function for , where , is
.
Verify that is a fixed point of .
And here is the question that I have no clue about (I don't need any help with the question above):
"2) Show further that the iteration satisfies
,
and deduce that
.
Hence show that as n approaches infinity if and only if .
Deduce that as approaches infinity if and only if .
Note: you might need to illustrate this conclusion graphically."