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You can approximate pi/4 with the Gregory and Leibniz series pi /4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 ........ (1)

btw it takes a lot of terms to get a reasonable approximation for pi.

The formuli is pi / 4 = [ ( -1 ) ^ ( k + 1 ) ] / ( 2 * k -1)

But there is another simpler equation.

pi / 4 = [ ( i ) ^ ( k - 1 ) ] / ( k )

where k = 1 2 3 4 5 ..... if we assume that simpler is better we get the terms 1/1 i/2 -1/3 -i/4 1/5 ...... or the same answer as (1) for pi / 4 in the real term and another number in the imaginary term .

To sum the terms of k = 1 to 10,000 using Matlab . I get 3.1413926 + 1.386094 * i .

So my question is, is there any significance to the number 1.386094?

(Yes i know it is simply the sum of the terms 1/2 - 1/4 + 1/6 - 1/8.....) but I am looking for something more.