This is a series that was made by me some days before.
This series gives us the area of a semi-circle. In the above series: 'r' represents the radius of the circle, n(r) is the numeric value of the radius, n(r) gives us the number of terms that we have to take inside the brackets, 'c' is a variable that has different values for different radii.
The inequality for 'c'
For radii = 2 and 3,
For other values of radius,
If we chose an appropriate value of 'c' as per the inequality, the series will give us a roughly accurate answer. If luckily we chose the right value of 'c' then the equation will give us an accurate answer.
For example, for radius = 2, the value of 'c' = 1.641 will give us an accurate answer.
Let us solve for the area of circle of radii = 2 cm .
Taking c =1.641 (as per the inequality)
Therefore, as per the series, we only take 2 terms inside the brackets as the numeric value of radius is 2.
further simplifying gives us the following result,
If we calculate the area of semicircle using,we get the area of semi-circle=6.28.
I hope you all liked this and I keenly look forward for your inputs and comments.