I need to find out how many terms it takes for the this series to converge to three decimal places of accuracy of Pi. e.i how many it terms it takes to obtain the value 3.141 from, the series: Leibniz series
I have tried various methods and they haven't seemed to work, but I have seen this formula which does work. However I do not know how to obtain the formula from the original series.
≈ 2 ⋅ ( 10^k − 1 )I would like to be able show how many terms it takes to get to the three decimal places of accuracy, from the original series. (The Leibniz series)