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 .

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.