Question

find the value of the summation.\\(\sum_{k=0}^{3} (k^2 + 3) = \square\\)

Explanation:

Step1: Expand the summation

Substitute $k=0,1,2,3$ into $k^2+3$:
$$\sum_{k=0}^{3} (k^2+3) = (0^2+3) + (1^2+3) + (2^2+3) + (3^2+3)$$

Step2: Calculate each term

Compute each individual term:
$$= (0+3) + (1+3) + (4+3) + (9+3)$$

Step3: Simplify each expression

Simplify the parentheses:
$$= 3 + 4 + 7 + 12$$

Step4: Sum the terms

Add all values together:
$$= 3+4=7; 7+7=14; 14+12=26$$

Answer:

26