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Abel's test for ∑???? to converge requires: ∑?? converges ?? is bounded ?? is monotone. Does...

Abel's test for ∑???? to converge requires:

∑?? converges
?? is bounded
?? is monotone.

Does it work it work if I claim: ∑???? converges if and only if, ∑?? converges, ?? is bounded, and ?? is monotone?

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