1/sqrt(n) convergent and divergent? why?

Answer 1

It converges to zero.

It is positive for all n>0

It is easy to show that it is strictly decreasing. Any strictly decreasing positive sequence must converge.

If you haven't had that theorem yet, you can prove it using limits. For any delta, you can find a value N such that 1/sqrt(N) < delta. (you can use algebra to do this). Since the function is decreasing, this is true for all n>N and you are done.

Answer 2

if n is positive,n=1,2,3,4,.....
the answer is divergent,as 1 divides by sqrt(n) becomes smaller n smaller until it reaches 0
if n is negative,then the equation is undefined.