If we repeat the process the result will be 1 , we have proved it below.
It is given that a even number is picked and divided by 2 , if it's odd multiply by 3 and add one. Repeating the process with the new number we will end at 1.
We have to prove this statement by picking a number.
What will be the value if 2 times of 12 is added to 2 ?
The value will be 2 × 12 + 2 or 24 + 2 or 26.
As per the question ;
Pick a number , if it is even , divide it by 2 , if it's odd multiply by 3 and add one.
Repeating the process with the new number we will end at 1.
We have to prove this.
Let's assume the number be 12.
i.e.,
n = 12
[tex]n_{1}[/tex] = 12 / 2 = 6
[tex]n_{2}[/tex] = 6 / 2 = 3
[tex]n_{3}[/tex] = 3 × 3 + 1 = 9 + 1 = 10
[tex]n_{4}[/tex] = 10 / 2 = 5
[tex]n_{5}[/tex] = 5 × 3 + 1 = 15 + 1 = 16
[tex]n_{6}[/tex] = 16 / 2 = 8
[tex]n_{7}[/tex] = 8 / 2 = 4
[tex]n_{8}[/tex] = 4 / 2 = 2
[tex]n_{9}[/tex] = 2 / 2 = 1
So , we have proved that the resulted number will be 1.
Thus , If we repeat the process the result will be 1 , we have proved it above.
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