Euler Transformation

number of terms

10

repeated Euler transformations

0

1

2

3

limit of infinite sequence

π

ln(2)

2

π =

4

1

-

4

3

+

4

5

-

4

7

+...

The Euler transformation can accelerate the convergence of an alternating infinite series by computing averages of each pair of successive partial sums in the sequence. This is equivalent to joining up the midpoints of the lines between each value when the partial sums of the sequence are plotted.