Answer:
<em>The whole series is: </em>
<em>3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4</em>
Step-by-step explanation:
<u>Inserting Numbers Between Two Given Endpoints</u>
Suppose we want to insert n equally-spaced numbers inside a given interval with endpoints [x,y].
To place n numbers, we need to open n+1 slots, at the end of which, a new number will be placed. The given interval is then divided into n+1 rational numbers of a value (y-x)/(n+1) each.
For example, let's add 6 rational numbers between 3 and 4. The width of the given interval is 4-3=1, and we need to place 6 numbers separated by 1/(6+1) = 1/7.
Start by the left endpoint:
3
The first number to add is 3+1/7=22/7
22/7
The second number to add is 22/7+1/7=23/7
23/7
The third number is 23/7+1/7=24/7
24/7
The next numbers follow the same pattern:
25/7
26/7
27/7
The last number is 28/7=4
4
The whole series is:
3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4
We have inserted 6 rational numbers between 3 and 4.
