Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#2
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Question
The sequence of values given by the iterative formula
With initial value , converges to
.
i. Use this iterative formula to find correct to 2 decimal places, giving the result of each iteration to 4 decimal places.
ii. State an equation that is satisfied by , and hence show that
.
Solution
i.
If we can write the given equation and transform it to
, then we can find the root of the equation by iteration method using sequence defined as.
We are already given iterative formula as;
If the sequence given by the inductive definition , with some initial value
, converges to a limit
, then
is the root of the equation
.
Therefore, if , then
is a root of
.
We are given initial value .
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It is evident that converges to
therefore
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The correct to 2 decimal places is
.
ii.
It is evident from (i) that can be written as;
We can manipulate this to find the value of .
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