已知求和式求新求和式的值的计算方法

### 📐解题思路 本题可根据求和运算的性质来求解\(\sum_{i = 3}^{100}(a[i] + 2*b[i])\)的值。 ### 🔍相关知识点 根据求和运算的性质可知：\(\sum_{i = m}^{n}(x[i]+y[i])=\sum_{i = m}^{n}x[i]+\sum_{i = m}^{n}y[i]\)，\(\sum_{i = m}^{n}k*x[i]=k*\sum_{i = m}^{n}x[i]\)（\(k\)为常数）。 ### 📝具体计算过程 - **步骤一：根据求和运算性质展开式子** 根据\(\sum_{i = m}^{n}(x[i]+y[i])=\sum_{i = m}^{n}x[i]+\sum_{i = m}^{n}y[i]\)，将\(\sum_{i = 3}^{100}(a[i] + 2*b[i])\)展开可得： \(\sum_{i = 3}^{100}(a[i] + 2*b[i])=\sum_{i = 3}^{100}a[i]+\sum_{i = 3}^{100}(2*b[i])\) - **步骤二：对\(\sum_{i = 3}^{100}(2*b[i])\)进行变形** 根据\(\sum_{i = m}^{n}k*x[i]=k*\sum_{i = m}^{n}x[i]\)（\(k\)为常数），可得\(\sum_{i = 3}^{100}(2*b[i]) = 2*\sum_{i = 3}^{100}b[i]\)。 所以\(\sum_{i = 3}^{100}(a[i] + 2*b[i])=\sum_{i = 3}^{100}a[i]+2*\sum_{i = 3}^{100}b[i]\)。 - **步骤三：代入已知条件计算结果** 已知\(\sum_{i = 3}^{100}a[i]=123\)，\(\sum_{i = 3}^{100}b[i]=321\)，将其代入上式可得： \(\sum_{i = 3}^{100}(a[i] + 2*b[i])=123 + 2*321\) \(=123 + 642\) \(= 765\) ######[AI问答 | 601点数解答 | 2026-05-01 15:32:48]