Use the divergence test to determine whether the following series diverges or state that the test is inconclusive. summation from k equals 0 to infinity startfraction 1 over 1000 plus k endfraction

The test is inconclusive.

Step-by-step explanation:

Let us assume that the series is . The Divergence Test tell us that, if the limit of the sequence defined by the general term of the series: , is different from zero, or it doesn't exist, then the series diverges.

In this exercise we have , then the limit we want to study is

It is not difficult to see that if grows to infinity,the limit of the given fraction is zero:

Thus, the convergence test is inconclusive. Recall the case of the harmonic series: , which is divergent and clearly .

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

step-by-step explanation: it is d