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Suppose convergent series Ak has partial sums: an And a series Bk has partial sums: bn...

Suppose convergent series Ak has partial sums: an
And a series Bk has partial sums: bn
Suppose lim(bn-an) =0, as n to infinity. Whether series Bk is converges or not? Prove.
Suppose lim(Bk-Ak) =0, as k to infinity. Whether series Bk is converges or not? Prove.
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