Determine if this series is convergent or divergent using the integral test $$\sum_{n=1}^{\infty} 1/n^{5/2}$$ I keep getting convergent the text book says its divergent. What am I doing wrong? I have determine that the function is positive, continuous, and decreasing by computing the derivative The integral of 1/n^(5/2) is convergent based on the p test 1/n^(p) where p1 is Convergent and p

Question

Determine if this series is convergent or divergent using the integral test

$$\sum_{n=1}^{\infty} 1/n^{5/2}$$

I keep getting convergent the text book says its divergent. What am I doing wrong?

I have determine that the function is 
positive, continuous, and decreasing by computing the derivative

The integral of 1/n^(5/2) is convergent based on the p test 

1/n^(p)
where
p>1 is Convergent
and
p < or = is Divergent

australopithecus · Answer

Correction
The integral of 1/n^(p) 

where 
p>1 
is Convergent 

and 

p < or = 1 
is Divergent

anonymous · Answer

might be there is misprinting in book

anonymous · Answer

The series is indeed convergent.

australopithecus · Answer

the derivative of n^(-5/2) is

-5/2n^(7/2) < 0
therefore the function is decreasing

australopithecus · Answer

ok It was the first time I applied this test so I wasn't 100% sure