Start with
1

1 + x
= 1 − x + x2x3 + x4x5 + …
Replacing x with x2 yields
1

1 + x2
= 1 − x2 + x4x6 + x8x10 + …
Integrating the both sides of the above gives
arctan x = x x3

3
+ x5

5
x7

7
+ x9

9
− …
Sub x = 1 in the above gives
arctan 1 = 1 − 1

3
+ 1

5
1

7
+ 1

9
− …
or
π

4
= 1 − 1

3
+ 1

5
1

7
+ 1

9
− …



File translated from TEX by TTH, version 4.03.
On 13 Jun 2022, 15:39.