Worksheet: Infinite Series

In this worksheet, we will practice representing an infinite series in sigma notation after defining it.

Q1:

Given that 𝑎=12, determine whether the infinite series is convergent or divergent.

  • AConvergent
  • BDivergent

Q2:

Given that 𝑥=𝑀+4, determine whether the infinite series is convergent or divergent.

  • ADivergent
  • BConvergent

Q3:

Express the series 12+14+16+18+ using sigma notation.

  • A1𝑛
  • B1𝑛
  • C1𝑛
  • D12𝑛
  • E12𝑛

Q4:

Which of the following series is not equivalent to 𝑏?

  • A𝑏+𝑏+𝑏
  • B𝑏+𝑏
  • C𝑏
  • D𝑏+𝑏+𝑏
  • E𝑏+𝑏+𝑏

Q5:

Which of the following is an equivalent expression for the infinite series 12𝑛?

  • A12+14+16+18+
  • B12+1+2+4+
  • C12+14+18+116+
  • D12+12+12+12+
  • E12+1+32+2+

Q6:

Express the series 𝑏+𝑏+𝑏++𝑏+ using sigma notation.

  • A𝑛
  • B𝑛
  • C𝑏
  • D𝑏
  • E𝑛

Q7:

Express the series (𝑛𝜋)+3cos using an index of 𝑛=0 instead of 𝑛=5.

  • A((𝑛+5)𝜋)+3cos
  • B((𝑛5)𝜋)+3cos
  • C𝑛𝜋5+3cos
  • D((𝑛5)𝜋)+3cos
  • E(5𝑛𝜋)+3cos

Q8:

Given that 𝑝=, determine whether the infinite series is convergent or divergent.

  • ADivergent
  • BConvergent

Q9:

Which of the following describes the relationship between an infinite series and a sequence?

  • AAn infinite series always takes the value of the largest term in an infinite sequence.
  • BAn infinite sequence is the sum of the terms in an infinite series.
  • CAn infinite series is the sum of the terms in an infinite sequence.
  • DAn infinite series is a sequence which has an infinite number of terms.
  • EAn infinite series is the product of the terms in an infinite sequence.

Q10:

Which of the following is an equivalent expression for the infinite series 𝑎?

  • A𝑎+𝑏+𝑐+𝑑+
  • B𝑎+𝑎+𝑎+𝑎+
  • C𝑎+𝑎+𝑎+𝑎+
  • D1+2+3+4+
  • E𝑎+𝑎+𝑎+𝑎+

Q11:

Express the series 𝑛+1𝑛 as a series that starts at 𝑛=3.

  • A𝑛+3(𝑛+2)
  • B𝑛+3(𝑛+3)
  • C𝑛1(𝑛2)
  • D3𝑛1𝑛
  • E3(𝑛+1)(3𝑛)

Q12:

Which of the following is an example of an infinite series?

  • A𝑎
  • B{𝑎}
  • C𝑎
  • Dlim𝑎
  • E{𝑎,𝑎,𝑎,,𝑎,}

Q13:

Given that 𝑎 is a constant, express the series 𝑎2+𝑎4+𝑎8+𝑎16+ using sigma notation.

  • A𝑎2𝑛
  • B𝑎2
  • C1𝑎2
  • D𝑎2𝑛
  • E𝑎2

Q14:

Which of the following series is equivalent to 𝑎𝑟?

  • A𝑎+𝑎𝑟()
  • B𝑎+𝑎𝑟
  • C𝑎+𝑎𝑟+𝑎𝑟
  • D𝑎+𝑎𝑟+𝑎𝑟()
  • E𝑎+𝑎𝑟

Q15:

Given that 𝑎 is a constant, which of the following is not an equivalent expression to the infinite series 5𝑎𝑛?

  • A1𝑛5𝑎
  • B1𝑎5𝑛
  • C5𝑎+54𝑎+59𝑎+516𝑎+
  • D51𝑎𝑛
  • E5𝑎1𝑛

Q16:

Which of the following series is equivalent to 5𝑒𝑒?

  • A5𝑒5𝑒+5𝑒𝑒
  • B5𝑒5𝑒+5𝑒𝑒
  • C1+5𝑒5𝑒+5𝑒𝑒
  • D5𝑒5𝑒+5𝑒𝑒
  • E5𝑒5𝑒+5𝑒𝑒

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