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Sequences and Series · Ages 16–17

Writing Series in Sigma Notation Practice

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For 11th-grade students. Express each series in sigma notation using the index variable k, starting at k = 1 unless instructed otherwise.

  1. Write the sum 1 + 2 + 3 + 4 + ... + 25 in sigma notation.

  2. Write the sum 3 + 6 + 9 + 12 + ... + 30 in sigma notation.

  3. Write the sum 5 + 9 + 13 + 17 + ... + 41 in sigma notation.

  4. Write the sum 1 + 4 + 9 + 16 + ... + 144 in sigma notation.

  5. Write the geometric series 2 + 6 + 18 + 54 + 162 in sigma notation.

  6. Write the alternating sum 4 - 8 + 12 - 16 + 20 in sigma notation.

  7. Write the series 1/2 + 2/3 + 3/4 + ... + 19/20 in sigma notation.

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Writing Series in Sigma Notation Practice

Answer key

  1. Write the sum 1 + 2 + 3 + 4 + ... + 25 in sigma notation.

    Sigma from k = 1 to 25 of k.

  2. Write the sum 3 + 6 + 9 + 12 + ... + 30 in sigma notation.

    Sigma from k = 1 to 10 of 3k.

  3. Write the sum 5 + 9 + 13 + 17 + ... + 41 in sigma notation.

    Sigma from k = 1 to 10 of (4k + 1).

  4. Write the sum 1 + 4 + 9 + 16 + ... + 144 in sigma notation.

    Sigma from k = 1 to 12 of k^2.

  5. Write the geometric series 2 + 6 + 18 + 54 + 162 in sigma notation.

    Sigma from k = 1 to 5 of 2*(3^(k - 1)).

  6. Write the alternating sum 4 - 8 + 12 - 16 + 20 in sigma notation.

    Sigma from k = 1 to 5 of ((-1)^(k + 1)) * 4k.

  7. Write the series 1/2 + 2/3 + 3/4 + ... + 19/20 in sigma notation.

    Sigma from k = 1 to 19 of k/(k + 1).