Question

Finding the indicated sum ,

Answer 1

This one can be solved without any cleverness.
\[\sum_{k=1}^{4}(-1)^k(k+11) =\]\[(-1)^1(1+11)+(-1)^2)(2+11)+(-1)^3)(3+11)+(-1)^4(4+11) =\]

Answer 2

Now why did I stick in those unwanted )'s?
\[(-1)^1(1+11)+(-1)^2(2+11)+(-1)^3(3+11)+(-1)^4(4+11) =\]
For odd k, \((-1)^k = -1\)
For even k, \((-1)^k = 1\)
-(1+11)+(2+11)-(3+11)+(4+11) =
all the alternating of signs cancels out the 11s, so it's just -1 + 2 - 3 + 4 = 2

Answer 3

How did you get the -1+2-3+4?

Answer 4

When I solved it I didnt get none of that, maybe I did it wrong?

Answer 5

\[-(1+11)+(2+11)-(3+11)+(4+11) = -1 -11 + 2 + 11 - 3 - 11 + 4 + 11\]
The alternating -11 + 11 sum to 0, leaving -1 + 2 - 3 + 4

Answer 6

Ah okay, I get it