Evaluate
7
Σ (-1)^k(k-1)
k=2
To evaluate the summation symbol Σ with the given expression, we need to substitute values of k in the given expression and then sum up those values.
Let's evaluate the expression for k=2:
(-1)^(2)(2-1) = (-1)^2(1) = 1(1) = 1
Next, evaluate the expression for k=3:
(-1)^(3)(3-1) = (-1)^3(2) = -1(2) = -2
Evaluate the expression for k=4:
(-1)^(4)(4-1) = (-1)^4(3) = 1(3) = 3
Continue this process until you reach the desired value of k. Then sum up all the evaluated values.
In this case, we need to evaluate the expression for k from 2 to 7 and then add them up:
Sum = 1 + (-2) + 3 + (-4) + 5 + (-6) + 7
To simplify the summation, we can rearrange the elements so that the positive and negative terms alternate:
Sum = 1 - 2 + 3 - 4 + 5 - 6 + 7
Group the positive terms and negative terms together:
Sum = (1 - 2) + (3 - 4) + (5 - 6) + 7
Simplifying each group:
Sum = -1 + -1 + -1 + 7
Combine the terms:
Sum = -3 + 7
Finally, add the terms together:
Sum = 4
Therefore, the evaluation of the given summation is 4.