1. **Problem:** Find the expanded form of $$\sum_{i=2}^5 2^{i-1}$$. 2. **Formula:** The summation $$\sum_{i=m}^n a_i$$ means adding terms from $$i=m$$ to $$i=n$$. 3. **Calculate each term:** - For $$i=2$$: $$2^{2-1} = 2^1 = 2$$ - For $$i=3$$: $$2^{3-1} = 2^2 = 4$$ - For $$i=4$$: $$2^{4-1} = 2^3 = 8$$ - For $$i=5$$: $$2^{5-1} = 2^4 = 16$$ 4. **Sum the terms:** $$2 + 4 + 8 + 16$$ 5. **Answer:** The expanded form is option (b) $$2 + 4 + 8 + 16$$.