How to , using Taylor series approximation , estimate the value of π, when arctan(x) ≈ x-x^3/3+x^5/5-x^7/7 ?

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Answer 1 · 2018-07-26T14:40:14

The value of #pi~=3.3396#

The Taylor approximation is

#arctan(x)=x-1/3x^3+x^5/5-x^7/7+x^9/9+....#

Let #x=1#

Then,

#Arctan(1)=1-1/3+1/5-1/7+1/9=0.8349#

But #arctan1=pi/4#

Therefore,

#pi/4=0.8349#

#pi=4*0.8349=3.3396#