In assessing normal distribution, I can see the pattern for the cumulative areas to the left of the corresponding sample values: 1/2n 3/2n 5/2n 7/2n and so on, that is:

numerator = odd numbers only (it seems)
denominator = 2 multiplied by the value of n

My question is why does the numerator consists of only odd numbers? How did this pattern come about? Why is the number 2 constant in the denominator? Does the pattern go on indefinitely?

Please help! I know it is easier to use the calculator but I really want to understand this concept!

Question

In assessing normal distribution, I can see the pattern for the cumulative areas to the left of the corresponding sample values: 1/2n 3/2n 5/2n 7/2n and so on, that is:

numerator = odd numbers only (it seems)
denominator = 2 multiplied by the value of n

My question is why does the numerator consists of only odd numbers? How did this pattern come about? Why is the number 2 constant in the denominator? Does the pattern go on indefinitely?

Please help! I know it is easier to use the calculator but I really want to understand this concept!