Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#3

Hits: 17

 

Question

The sequence defined by

,

Converges to the value .

     i.       Find the value of correct to 3 decimal places. Show your working, giving each calculated  value of the sequence to 5 decimal places.

   ii.       Find, in the form , an equation of which is a root.

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 .

1

2

3

4

5

6

7

8

9

10

11

12

It is evident that  converges to  therefore .

The correct to 3 decimal places is .


ii.

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 have already found the root of the equation as .

This has been found for the equation  Therefore;

Please follow and like us:
error0

Comments