Mathematics

Mathematics

Problem

## EXPLORATION 1 Summing with Sigma Sigma notation is actually even more versatile than the definition above suggests. See if you can determine the number represented by each of the following expressions. 1. ∑k=153k\sum_{k=1}^{5} 3 k 2. ∑k=58k2\sum_{k=5}^{8} k^{2} 3. ∑n=012cos⁡(nπ)\sum_{n=0}^{12} \cos (n \pi) 4. ∑n=1∞sin⁡(nπ)\sum_{n=1}^{\infty} \sin (n \pi) 5. ∑k=1∞310k\sum_{k=1}^{\infty} \frac{3}{10^{k}} (If you're having trouble with number 5, here's a hint: Write the sum as a decimal!) a. ∑k=153k\sum_{k=1}^{5} 3 k b. ∑k=58k2\sum_{k=5}^{8} k^{2} c. ∑n=012cos⁡(nπ)\sum_{n=0}^{12} \cos (n \pi) d. ∑n=1∞sin⁡(nπ)\sum_{n=1}^{\infty} \sin (n \pi) e. ∑k=1∞310k\sum_{k=1}^{\infty} \frac{3}{10^{k}}

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