Question

Express the series using sigma notation. -8 + 4 - 2 + 1.

Answer 1

Option a.
`\sum_(k=0)^(k=3)(-2)^(3-k)`.

Explanation:

In this question the given series is -8 + 4 - 2 + 1...

which can be written as
`-2^(3)+2^(2)-2^(1)+2^(0)`

Or
`-2^((3-0))+2^((3-1))-2^((3-2))+2^((3-3))`

Here the expression are ranging from 0 to 3.

Now we can see that it's an exponential series

Now we write it in the form of sigma notation

`=\sum_(k=0)^(k=3)(-2)^(3-k)`

So the answer is Option a.
`\sum_(k=0)^(k=3)(-2)^(3-k)`