Answer to Question #308416 in Real Analysis for Pankaj

Question

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

Answer 1

False

Let the two sequences be X and Y:

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 and not a divergent sequence