How do i solve the following summation problem?
1 Answer
May 9, 2018
There are few enough terms to just do it.
sum_(n=4)^(11) (30 - 4n)
= (30 - 4(4)) + (30 - 4(5)) + (30 - 4(6)) + (30 - 4(7)) + (30 - 4(8)) + (30 - 4(9)) + (30 - 4(10)) + (30 - 4(11))
From term 4 through 11 inclusive, there are
= 8(30) - 4(4) - . . . - 4(11)
= 8(30) - 4(4 + . . . + 11)
We know that
4 + . . . + 11 = 1 + . . . + 11 - (1 + 2 + 3)
= 66 - 1 - 2 - 3 = 60 .
Therefore,
sum_(n=4)^(11) (30 - 4n) = 240 - 240 = color(blue)(0)