Sigma Notation Worksheet with Answer Key

What's on the worksheet

1. For each sum, say how many terms it has.
   \sum_{k=1}^{4} (7 - 3k)\sum_{m=2}^{6} (m^2 + 1)\sum_{j=1}^{4} (-1)^j \cdot 3 \cdot 2^{j}\sum_{k=0}^{3} \dfrac{k}{k + 1}\sum_{k=-2}^{2} k^3
2. Write each sum in sigma notation, with the index starting at 1.
   −11 + (−4) + 3 + 10 + … + 6650 + 46 + 42 + … + 2243 + 162 + 108 + … + 321 + 8 + 27 + 64 + 125 + 216\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \cdots + \dfrac{1}{256}
3. Rewrite _k=4^15 (2k - 1) so that the index starts at 1.
4. Suppose _k=1^15 a_k = 68 and _k=1^9 a_k = 28.
5. You are told that _k=1^8 k = 36 and _k=1^8 k² = 204.
6. A student wants to rewrite _k=1^9 (4k - 1) so that the index starts at 0.