Answer:
Step-by-step explanation:
Sigma notation is:
n
∑ ak
k=1
The n on top is the number of terms. ak is the expression for the kth term.
Let's look at the first one. The series is:
-2+4+-8+...+64+-128
There's two things to notice. One, the sign changes back and forth between + and -. Two, the magnitude doubles with each next term. Therefore:
ak = (-2)ᵏ
Next we need to find the number of terms. -128 is the last term, so:
128 = 2ⁿ
n = 7
So the answer is:
7
∑ (-2)^k
k=1
Now the second one. Notice the numerators are all 1 and the denominators are all perfect squares. Therefore:
ak = (1/k)²
The last term is 1/100, so n = 10.
So the answer is:
10
∑ (1/k)²
k=1
Now the last one. Notice that each term is 5 plus the previous term. This is an arithmetic series. So we can say:
ak = 4 + 5(k-1)
ak = 4 + 5k - 5
ak = 5k - 1
The last term is 49, so:
49 = 5n - 1
n = 10
So the answer is:
10
∑ (5n-1)
k=1
