Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 10·(1/4)ᵏ.

a = 10r = 1/4k₀ = 0
S =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=0∞ 8·(2/5)ᵏ.

a = 8r = 2/5k₀ = 0
S =
3.Medium
xx₀ = −1??R

The power series Σk=1∞ k²·2ᵏ·(x + 1)ᵏ converges on an interval around x₀ = −1. Find the right end x of that interval.

Σ k²·2ᵏ·(x + 1)ᵏx₀ = −1
x =
4.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 12/(k(k + 2)).

ak = 12/(k(k + 2))
S =
5.Hard

Recognise the series and find its sum: S = Σk=1∞ k·(−0.5)ᵏ.

ak = k·(−0.5)ᵏ
S =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ (−1)k+1·0.5ᵏ/k.

ak = (−1)k+1·0.5ᵏ/k
S =

Answer key

  1. 1. S = 13.33
  2. 2. S = 13.33
  3. 3. x = −0.5
  4. 4. S = 9
  5. 5. S = −0.2222
  6. 6. S = 0.4055

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