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 𝑎 𝑏 .

  • Afalse
  • Btrue

Q2:

True or False: If 𝑎 0 and 𝑏 0 and the series 𝑎 and 𝑏 both converge, then so does 𝑎 𝑏 .

  • Afalse
  • Btrue

Q3:

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

  • ATrue
  • BFalse

Q4:

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

  • ATrue
  • BFalse

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