Taylor series: a series expansion of a function about a point

(3) x – x3/3 + x5/5 – x7/7 + … = arctan x. by antidifferentiating. (Check: If we differentiate the left hand side of (3) term-by-term, we get the left hand side of (2). Likewise if we differentiate arctan x, we get 1/(1+x2). So the LHS and RHS of (3) have the same derivative.) Now substituting x = 1 into (3) we get ................
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