Use the properties of summation and Theorem 5.2 to evaluate the sum. $$\sum _ { i = 1 } ^ { 37 } ( i - 6 ) ^ { 2 }$$
A) $9,176$
B) 10,471
C) 18,907
D) $9,139$
E) 98,346

Question

Quizplus · Accepted Answer

The sum $\sum _ { i = 1 } ^ { 37 } ( i - 6 ) ^ { 2 }$ can be evaluated by recognizing it as a sum of squares with a shift. The formula for the sum of squares is $\sum _ { i = 1 } ^ { n } i^2 = \frac{n(n + 1)(2n + 1)}{6}$. Applying this formula and adjusting for the shift, we find the sum equals 10,471.

Use the Properties of Summation and Theorem 5 ∑i=137(i−6)2\sum _ { i = 1 } ^ { 37 } ( i - 6 ) ^ { 2 }i=1∑37​(i−6)2

Use the Properties of Summation and Theorem 5 $\sum _ { i = 1 } ^ { 37 } ( i - 6 ) ^ { 2 }$