Question

If f(x) = 3x22, evaluate afI: ()k=1

Answer 1

Step 1: Write out the function given

`f(x)=3x^2-x`

Step 2: Interprete the question given

`\sum ^5_(k\mathop=1)f((k)/(2))`

The question requested we find the summation of the first five terms for f(k/2), when k is 1, 2, 3, 4, and 5

Step 3: Find the expression for f(k/2)

`\begin{gathered} f((k)/(2))=3((k)/(2))^2-(k)/(2) \\ =(3k^2)/(4)-(k)/(2) \\ =(3k^2-2k)/(4) \end{gathered}`
`\begin{gathered} =(3(1)^2-2(1))/(4)+(3(2)^2-2(2))/(4)+(3(3)^2-2(3))/(4)+(3(4)^2-2(4))/(4)+(3(5)^2-2(5))/(4) \\ =(1+8+21+40+65)/(4) \\ =(135)/(4) \\ =33.75 \end{gathered}`

Hence, the answer is 33.75