What if the problem asked for $$ \sum_{k=3}^{5}(k-2)(k-3) $$

Question

UpStudy AI · Accepted Answer

To evaluate the sum $$ \sum_{k=3}^{5}(k-2)(k-3) $$, we will first calculate the expression $$(k-2)(k-3)$$ for each integer $$k$$ from 3 to 5.

1. For $$k = 3$$:
   $$
   (3-2)(3-3) = (1)(0) = 0
   $$

2. For $$k = 4$$:
   $$
   (4-2)(4-3) = (2)(1) = 2
   $$

3. For $$k = 5$$:
   $$
   (5-2)(5-3) = (3)(2) = 6
   $$

Now, we can sum these results:
$$
\sum_{k=3}^{5}(k-2)(k-3) = 0 + 2 + 6 = 8
$$

Thus, the value of the sum is:
$$
\boxed{8}
$$
The sum $$ \sum_{k=3}^{5}(k-2)(k-3) $$ equals 8.

What if the problem asked for \( \sum_{k=3}^{5}(k-2)(k-3) \)