Worksheet: Operations on Series

In this worksheet, we will practice discussing the convergence or divergence of a combination of two series.

Q1:

True or False: If the series 𝑎 and 𝑏 both converge, then so does 𝑎𝑏.

  • Atrue
  • Bfalse

Q2:

True or False: If 𝑎0 and 𝑏0 and the series 𝑎 and 𝑏 both converge, then so does 𝑎𝑏.

  • Afalse
  • Btrue

Q3:

True or False: If 𝑎𝑏 converges, then so do the series 𝑎 and 𝑏.

  • AFalse
  • BTrue

Q4:

True or False: If 𝑎 and 𝑏 are divergent, then (𝑎+𝑏) must also be divergent.

  • AFalse
  • BTrue

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