Compute the product (-39 + 13)*(-36 + 12) *(-33 + 11) *(-30 + 10) ---(33 -11)* (36 - 12) *(39 - 13) ]Where the first summand in each factor is increasing by 3 and the second summand is decreasing by 1. please help asap.
Your product is
product(k=0..26) ((-39+3k)+(13-k))
= product(k=0..26)(2k-26)
when k=13 the factor will be zero.
so the solution is 13?
To compute the given product, let's break it down step by step:
1. First, let's calculate all the individual factors in the product:
Factor 1 = (-39 + 13) = -26
Factor 2 = (-36 + 12) = -24
Factor 3 = (-33 + 11) = -22
Factor 4 = (-30 + 10) = -20
Factor 5 = (33 - 11) = 22
Factor 6 = (36 - 12) = 24
Factor 7 = (39 - 13) = 26
2. Now, let's multiply all the factors together:
(-26) * (-24) * (-22) * (-20) * 22 * 24 * 26
We can start by calculating the product of the absolute values, as the negatives will cancel each other out:
(26) * (24) * (22) * (20) * 22 * 24 * 26
3. Group the factors that are the same:
(26 * 26) * (24 * 24) * (22 * 22) * (20 * 20) * (22 * 24)
4. Calculate the grouped factors:
676 * 576 * 484 * 400 * 528
5. Finally, multiply all the grouped factors together:
676 * 576 * 484 * 400 * 528 = 25,147,889,920
Therefore, the product of the given expression is 25,147,889,920.