# Gregory Series

Gregory Series

The Gregory series, , is a slowly converging formula for found in the 1670s by James Gregory and Gottfried Wilhelm Leibniz, each working independently. It is obtained by substituting into the Leibniz series . The number near on the circle is the last term added.

1-+-+…

1

3

1

5

1

7

π

4

x=1

arctan(x)=

∞

∑

k=1

k+1

(-1)

k+1

x

2k-1

π

4