# How do you test the alternating series #Sigma (-1)^nsqrtn/(n+1)# from n is #[1,oo)# for convergence?

##### 1 Answer

The series:

is convergent

#### Explanation:

The series:

is an alternating series, so we can test its convergence using Leibniz's theorem, which states that an alternating series

is convergent if:

(i)

#lim_(n->oo) a_n = 0# (ii)

#a_(n+1) <= a_n#

in our case:

so the first condition is satisfied.

For the second we analyze the function:

and calculate the derivative:

we can see that

that is:

and also the second condition is satisfied.