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It is known that power series expansion of certain functions such as sech(x) diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of sech(x) that is convergent for all x. The convergent series is a sum of the Taylor series of sech(x) and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finitedoi:10.1155/2018/6043936 fatcat:bjhxy5fexbewlni2ht6hi37wqa