Question

Complete the statements about the series

There are

The sign of each term in the series

Answer 1

Answer: 5 and Alternates

Explanation:

Answer 2

Ok, first in our series we can see two numbers in the Sigma, one bellow 0, and other above, 4.

This means that the value of k will go from 0 to 4, then all the numbers in the sum are:

(-1/2)^0 + (-1/2)^1 + (-1/2)^2 + (-1/2)^3 + (-1/2)^4

So we have 5 terms in our series.

b) to see the sign in each term, we must solve the powers, remember that:

(-1)^n is -1 if n is odd, and is equal to 1 if n is even, so we have:

(-1/2)^0 + (-1/2)^1 + (-1/2)^2 + (-1/2)^3 + (-1/2)^4

= 1 -1/2 + 1/4 - 1/8 + 1/16.

So the sign in each term of the series alternates.