Worksheet: Infinite Series in Sigma Notation

In this worksheet, we will practice calculating the sum of an infinite geometric series in sigma notation.

Q1:

Evaluate 𝑟 = 8 𝑟 1 3 5 4 1 2 .

  • A 3 5 2 5 6
  • B The series is divergent so it has no sum.
  • C 3 5 7 6 8
  • D 3 5 7 6 8
  • E 3 5 2 4

Q2:

Evaluate 𝑟 = 4 𝑟 1 5 9 ( 3 ) .

  • A 1 5 2
  • B 1 5 4
  • C 1 5 4
  • D The series is divergent so it has no sum.
  • E 5 3 2 4

Q3:

Evaluate 𝑟 = 2 𝑟 1 4 3 ( 2 ) .

  • A 8 3
  • B 8 9
  • C 8 9
  • D The series is divergent so it has no sum.
  • E 4 2 9 7

Q4:

Evaluate 𝑟 = 5 𝑟 1 5 0 1 7 ( 2 ) .

  • A 8 0 0 1 7
  • B 8 0 0 5 1
  • C 8 0 0 5 1
  • D The series is divergent so it has no sum.
  • E 5 0 8 6 7

Q5:

Evaluate 𝑟 = 3 𝑟 1 2 4 1 4 .

  • A2
  • B The series is divergent so it has no sum.
  • C 6 5
  • D 6 5
  • E 9 6 5

Q6:

Evaluate 𝑟 = 1 𝑟 1 2 8 9 .

  • A 1 8 1 7
  • B The series is divergent so it has no sum.
  • C 1 8
  • D18
  • E 9 1 0

Q7:

Evaluate 𝑟 = 2 𝑟 1 2 3 6 5 .

  • A4
  • B 4 1 1
  • C 4 1 1
  • D The series is divergent so it has no sum.
  • E 5 7 9 2

Q8:

Evaluate 𝑟 = 2 𝑟 1 3 9 1 4 8 7 .

  • A 1 5 6 7
  • B 5 2 3 5
  • C 5 2 3 5
  • D The series is divergent so it has no sum.
  • E 1 3 1 4 0

Q9:

Evaluate 𝑟 = 1 𝑟 1 7 4 1 2 .

  • A 7 6
  • B The series is divergent so it has no sum.
  • C 7 2
  • D 7 2
  • E 7 1 6

Q10:

Evaluate 𝑟 = 1 𝑟 1 2 9 2 0 2 5 .

  • A 2 9 1 2
  • B The series is divergent so it has no sum.
  • C 2 9 2 8
  • D 2 9 2 8
  • E 2 9 5 6 0

Q11:

Evaluate 𝑟 = 4 𝑟 1 1 1 6 4 3 .

  • A 4 6 3
  • B 4 9
  • C 4 9
  • D The series is divergent so it has no sum.
  • E 1 2 5 6

Q12:

Evaluate 𝑟 = 1 𝑟 1 3 5 6 7 .

  • A 2 1 6 5
  • B The series is divergent so it has no sum.
  • C 2 1 5
  • D 2 1 5
  • E 7 7 5

Q13:

Evaluate 𝑟 = 2 𝑟 1 5 3 9 7 .

  • A 1 5 2
  • B 1 5 1 6
  • C 1 5 1 6
  • D The series is divergent so it has no sum.
  • E 5 1 4 4

Q14:

Evaluate 𝑟 = 1 𝑟 1 5 2 1 5 .

  • A 2 5 1 2
  • B The series is divergent so it has no sum.
  • C 2 5 8
  • D 2 5 8
  • E 2 5 1 6

Q15:

Evaluate 𝑟 = 1 𝑟 1 1 4 9 2 3 .

  • A 1 4 3
  • B The series is divergent so it has no sum.
  • C 1 4 1 5
  • D 1 4 1 5
  • E 1 4 4 0 5

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