Comparison test?

Question

i'm having some problem understanding this concept, i dont like posting my assignments on here but i need help desperately.

summation n= 2 to infinity (SQRT n/ n-1). determine whether the series is convergent or divergent.

Answer 1

If your series is sqrt(n/(n-1)), the series diverges because limit of the n-th term (as n -> inf) = 1. (Recall if the limit is not 0, the series must diverge.)

If your seriies is (sqrt (n))/(n-1), then you can use the comparison test with 1/(2*sqrt(n)) (which is divergent by the p-series test). Clearly (sqrt (n))/(n-1) >= 1/(2*sqrt (n)), so (sqrt (n))/(n-1) diverges.