Convergence of Infinite Series - A Review

Abstract

This paper reviews the methods to select correct tests for checking the convergence or divergence of infinite series. To check the convergence or divergence of a series, there are various methods like Power Test, Comparison Test, Root Test, Ratio Test, Gauss Test etc. and the conditions and methods to apply these tests are explained here. Only the correct use of these tests gives us the valid results about the behavior of a series.

  KEY WORDS: Convergent, Divergent; Oscillates; artial Sums; Alternating Series; Harmonic Series; Geometric series; Power Series.