Knowing the following Series:
Then, 
Now 
, in circular
measure so that 
.
Since tan 0 = 0, 
,
so that when x = 0 in the above series 
and
C = 0. Hence:
Pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ....
We may group the terms in pairs in two ways:
Alternatively:
Then we see that, 2/3 < Pi/4 < 1, so that 2.6 < Pi < 4
We can get a much more convenient form by using other values of tan a. For instance tan (30):
Then if a = pi/6,
{
}
Then Pi = 3.14....
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