What is a convergent sequence and a divergent sequence?

If sequence {an} is divergent and {bn} is convergent, is the squence {an-bn} divergent?

  • if sequence {an} is divergent and {bn} is convergent, is the squence {an-bn} divergent?

  • Answer:

    Yes. If {(a-b)(n)} were also convergent, then since {a(n)} = {b(n)} + {(a-b)(n)} would also have to converge, which is a contradiction. I hope this helps!

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