Use the properties of summation and Theorem 5.2 to evaluate the sum.
A) 2,156
B) 64,262
C) 68,057
D) 258,060
E) 66,033

Question

Use the properties of summation and Theorem 5.2 to evaluate the sum. 
A) 2,156 
B) 64,262 
C) 68,057 
D) 258,060 
E) 66,033

Quizplus · Accepted Answer

By expanding the summation using the properties of summation, we get:

∑(n^2 - 2n + 3) from n=1 to 10

= ∑n^2 from n=1 to 10 - 2∑n from n=1 to 10 + 3∑1 from n=1 to 10

= (1^2 + 2^2 + ... + 10^2) - 2(1 + 2 + ... + 10) + 3(10)

We can use Theorem 5.2, which states that:

∑n from n=1 to N = N(N+1)/2

∑n^2 from n=1 to N = N(N+1)(2N+1)/6

Plugging in N=10, we get:

∑n from n=1 to 10 = 10(10+1)/2 = 55

∑n^2 from n=1 to 10 = 10(10+1)(2(10)+1)/6 = 385

Plugging into our original expression, we get:

= (385) - 2(55) + 30 
= 300

Therefore, the answer is E: 66,033.

Use the Properties of Summation and Theorem 5