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Sigma notation worksheets Grades 11–12

Evaluate sums written in sigma notation.

The front of the free sigma notation worksheet
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Free · Worked example · 30 problems · Answer key · US Letter

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How to do it

Σ means add. Put in each value of k from the bottom number to the top number, then add the results.

∑k=15(5k+2)=85\sum_{k = 1}^{5}(5k + 2) = 85
7+12+17+22+27=857 + 12 + 17 + 22 + 27 = 85put in k = 1, 2, …, 5 and add

Example problems

  1. ∑k=043k=\sum_{k = 0}^{4}3ᵏ =
  2. ∑k=28(k2+1)=\sum_{k = 2}^{8}(k^{2} + 1) =
  3. ∑k=05(−2k−6)=\sum_{k = 0}^{5}(-2k - 6) =
  4. ∑k=163k=\sum_{k = 1}^{6}3ᵏ =

Sequences and series

  1. Arithmetic sequences
  2. Geometric sequences
  3. Writing the formula for a sequence
  4. Sigma notation
  5. Arithmetic series
  6. Geometric series
  7. Infinite geometric series
  8. Combinations (nCk)
  9. The binomial theorem