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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