evaluate exactly
it's a sigma notation where
n=20
k=1
and
(1+(-1)^k)
To evaluate the given sigma notation, we can substitute the values of n and k into the expression (1+(-1)^k) and iterate through the values of k from 1 to 20.
Let's calculate the expression for each value of k and find the sum of the resulting values.
1. Start with k = 1:
(1+(-1)^1) = 1 + (-1) = 0
2. Moving to k = 2:
(1+(-1)^2) = 1 + 1 = 2
3. For k = 3:
(1+(-1)^3) = 1 + (-1) = 0
4. Continue this process for k = 4 to k = 20, alternating between 0 and 2 for each value of k.
Now, let's calculate the sum of these values:
0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 + 0 + 2 = 20
Therefore, the evaluated value of the sigma notation (1+(-1)^k) when n = 20 and k ranges from 1 to 20 is 20.