시그마 성질

$\displaystyle \sum\limits _{k = 1} ^{7} \left( a _{k} + k \right) = 50$에서 $\displaystyle \sum\limits _{k = 1} ^{7} a _{k} + \sum\limits _{k = 1} ^{7} k = 50$ $\therefore$$\displaystyle \sum\limits _{k = 1} ^{7} a _{k}$$\displaystyle = 50 - \sum\limits _{k = 1} ^{7} k$$\displaystyle = 50 - \frac{7 \times 8}{2} = 22$ $\displaystyle \sum\limits _{k = 1} ^{7} \left( a _{k} + 2 \right) ^{2} = 300$에서 $\displaystyle \sum\limits _{k = 1} ^{7} \left( a _{k} ^{2} + 4 a _{k} + 4 \right) = 300$ $\displaystyle \sum\limits _{k = 1} ^{7} a _{k} ^{2} + 4 \sum\limits _{k = 1} ^{7} a _{k} + \sum\limits _{k = 1} ^{7} 4 = 300$ $\therefore$$\displaystyle \sum\limits _{k = 1} ^{7} a _{k} ^{2}$$= 300 - 4 \times 22 - 7 \times 4$$= 184$