Answer to Question #175362 in Real Analysis for Anand

Question #175362

The product of two divergent sequences is divergent. True or false? Justify.


1
Expert's answer
2021-05-05T19:41:56-0400

The product of two divergent sequences is divergent "\\implies" it is a False statement

Counter example:

Let two sequences: X = (1, 0, 2, 0, 3, 0, ............. )

Y = (0, 1, 0, 2, 0, 3, ..............)

clearly, both sequences are unbounded and diverging to "\\infty"

there product X"\\cdot"Y = (0, 0, 0, 0, 0, 0, .........)

which is a constant sequence converging to 0

therefore,

X"\\cdot"Y is a convergent sequence.


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