We, somehow, tried to use the next identity:
-[k+1 / 2] = [-k+1 / 2]
Is this result true or false? If it is true, prove it; if it is false, provide the actual value of the righthand side that makes the identity true. Hint: you can try some numerical values to see how the
equations works.
If you meant
-(k+1)/2 = (-k+1)/2
that is certainly not true, because it's the same as
-(k+1) = -k+1
-k-1 = -k+1
-1 = 1
same holds if you just meant
-(k + 1/2) = -k + 1/2
Thank you.
To determine if the given identity is true or false, we will examine it by using numerical values. Let's consider some values for "k" and evaluate both sides of the equation to see if they are equal.
Let's assume k = 2:
-[2 + 1 / 2] = [-2 + 1 / 2]
Simplifying both sides, we get:
-3/2 = -1/2
These two sides are equal, so the identity holds true for k = 2.
Let's now assume k = 5:
-[5 + 1 / 2] = [-5 + 1 / 2]
Simplifying both sides, we get:
-6/2 = -4/2
These two sides are equal again, so the identity holds true for k = 5.
Now let's assume k = -1:
-[-1 + 1 / 2] = [1 + 1 / 2]
Simplifying both sides, we get:
-1/2 = 3/2
The two sides are not equal, therefore the given identity is false for k = -1.
Since we have found a value for k that makes the equation false, we can conclude that the given identity is not true for all values of k. The actual value of the right-hand side that makes the identity true is 3/2 when k = -1.