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Worksheet: Infinite Series in Sigma Notation

Q1:

Evaluate ∞ π‘Ÿ = 4 π‘Ÿ βˆ’ 1 ο„š 5 9 ( βˆ’ 3 ) .

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

Q2:

Evaluate ∞ π‘Ÿ = 2 π‘Ÿ βˆ’ 1 ο„š 4 3 ( βˆ’ 2 ) .

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

Q3:

Evaluate ∞ π‘Ÿ = 5 π‘Ÿ βˆ’ 1 ο„š 5 0 1 7 ( βˆ’ 2 ) .

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

Q4:

Evaluate ∞ π‘Ÿ = 3 π‘Ÿ βˆ’ 1 ο„š 2 4 ο€Ό βˆ’ 1 4  .

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

Q5:

Evaluate ∞ π‘Ÿ = 8 π‘Ÿ βˆ’ 1 ο„š 3 5 4 ο€Ό βˆ’ 1 2  .

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

Q6:

Evaluate ∞ π‘Ÿ = 1 π‘Ÿ βˆ’ 1 ο„š 2 ο€Ό 8 9  .

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

Q7:

Evaluate ∞ π‘Ÿ = 2 π‘Ÿ βˆ’ 1 ο„š 2 3 ο€Ό βˆ’ 6 5  .

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

Q8:

Evaluate ∞ π‘Ÿ = 2 π‘Ÿ βˆ’ 1 ο„š 3 9 1 4 ο€Ό βˆ’ 8 7  .

  • A 1 5 6 7
  • B βˆ’ 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 ∞ π‘Ÿ = 1 π‘Ÿ βˆ’ 1 ο„š 7 4 ο€Ό 1 2  .

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

Q10:

Evaluate ∞ π‘Ÿ = 1 π‘Ÿ βˆ’ 1 ο„š 2 9 2 0 ο€Ό βˆ’ 2 5  .

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

Q11:

Evaluate ∞ π‘Ÿ = 4 π‘Ÿ βˆ’ 1 ο„š 1 1 6 ο€Ό 4 3  .

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

Q12:

Evaluate ∞ π‘Ÿ = 1 π‘Ÿ βˆ’ 1 ο„š 3 5 ο€Ό 6 7  .

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

Q13:

Evaluate ∞ π‘Ÿ = 2 π‘Ÿ βˆ’ 1 ο„š 5 3 ο€Ό βˆ’ 9 7  .

  • A 1 5 2
  • B βˆ’ 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 ∞ π‘Ÿ = 1 π‘Ÿ βˆ’ 1 ο„š 5 2 ο€Ό 1 5  .

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

Q15:

Evaluate ∞ π‘Ÿ = 1 π‘Ÿ βˆ’ 1 ο„š 1 4 9 ο€Ό βˆ’ 2 3  .

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