Question

Which letter is correctcalculate the sum ∑_(i=1)^4 〖5(4i-1)〗^2/4 (hint: expand the sum)

Answer 1

Given:

The sum is,

`\sum ^4_(i=1)(5(4i-1)^2)/(4)`

Expand the sum,

`\begin{gathered} \sum ^4_(i=1)(5(4i-1)^2)/(4)=(5(4(1)-1)^2)/(4)+(5(4(2)-1)^2)/(4)+(5(4(3)-1)^2)/(4)+(5(4(4)-1)^2)/(4) \\ =(5(3)^2)/(4)+(5(7)^2)/(4)+(5(11)^2)/(4)+(5(15)^2)/(4) \\ =(45)/(4)+(245)/(4)+(605)/(4)+(1125)/(4) \\ =(2020)/(4) \end{gathered}`

Answer: option b)

`(2020)/(4)`