Question

1. (0 points) evaluate the sum. write your answer as a whole number or a fraction.

(a)
\\\sum_{k=0}^{3} (-1)^{k+1} 2^k\\

(b)
\\\sum_{k=3}^{8} k(k+1)\\

Explanation:

Step1: Expand the first sum

$$\sum_{k=0}^{3} (-1)^{k+1} 2^k = (-1)^1 2^0 + (-1)^2 2^1 + (-1)^3 2^2 + (-1)^4 2^3$$

Step2: Calculate the first sum

$$-1 + 2 - 4 + 8 = -5$$

Step3: Expand the second sum

$$\sum_{k=3}^{8} k(k+1) = 3(4) + 4(5) + 5(6) + 6(7) + 7(8) + 8(9)$$

Step4: Calculate the second sum

$$12 + 20 + 30 + 42 + 56 + 72 = 234$$

Answer:

(a) \(-5\)
(b) \(234\)