Question

Can Someone Help me with my Algabra 2 Homework 4a-c​

Answer 1

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