1. **State the problem:** Compute the sum $$\sum_{k=2}^5 (2k+1)$$. 2. **Formula and explanation:** The summation $$\sum_{k=a}^b f(k)$$ means adding the values of the function $$f(k)$$ for each integer $$k$$ from $$a$$ to $$b$$ inclusive. 3. **Apply the formula:** Here, $$f(k) = 2k + 1$$, and we sum from $$k=2$$ to $$k=5$$. 4. **Calculate each term:** - For $$k=2$$: $$2(2) + 1 = 4 + 1 = 5$$ - For $$k=3$$: $$2(3) + 1 = 6 + 1 = 7$$ - For $$k=4$$: $$2(4) + 1 = 8 + 1 = 9$$ - For $$k=5$$: $$2(5) + 1 = 10 + 1 = 11$$ 5. **Sum the terms:** $$5 + 7 + 9 + 11 = 32$$ 6. **Final answer:** $$\sum_{k=2}^5 (2k+1) = 32$$.