An iterative algorithm is said to converge if its results gradually vary less and become closer and closer to some final value. Not that the former does not imply the latter, for example in the sum 1+1/2+1/3+1/4... the partial answers get closer and closer to each, but the sum does not converge to a final value. In contrast the sum 1+1/2+1/4+1/8... does converge as the partial sums values get closer and closer (but never reach) to the value 2.
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