Look at the following sum. 1 + 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64. .

Because this is an infinite sequence, we can use the following formula:

a1/r

a1 is the first number in the sequence, r is the rate of change.

To find r, we do the second value divided by the first. So

1/2 / 1 = 1/2
r = 1/2

Now we plug in to our equation.

1 / 1/2

= 2

So your sum is 2

I hope this Helps!

Step-by-step explanation:

Step1: find the interval of roots. Consider -3 and -2

Hence, the root must be on [-3,-2]

Step2:  consider the middle point -2.5

Then, the root must be on [-3, -2.5]

Step 3: Repeat step 2 by finding the value of f at the middle point -2.75

Step 3: Repeat step 2 by finding the value of f at the middle point of the interval [-2.75,-2.5] which is -2.625

Step4: Repeat step 2 on [-2.75, -2.625]

Repeat step 2 until you got the root which is -2.701