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Infinite series and its convergence are basic concepts to know mathematics from very beginning of primary stage. It revolves in the minds of mathematicians all along life and creats visionary power to estimate everything that comes in the mind. This estimation is called approximation if put on sound footings with axioms. So every measurement by naked eye or ear or by sophisticated instruments is merely an approximation. It is hoped that in this monograph, approximation by wavelets will be useful in technology and communication science in coming days.