Answer these Ratio Test Questions Correctly to earn Best Answer!?

Question

Use the ratio test to decide if the series converges or diverges.

Let L be the limit obtained when applying the ratio test. Determine the value of L.

1) Infinity(Sigma),n=0 ((n^3)+1)/(2^n)
2) Infinity(Sigma),n=1 (2n)!/((n!)(n+3)!)
3) Infinity(Sigma),n=2 (3)/sqrt(n)

Does these series:
A) Converge
B) Diverge
C) The ratio test does not tell us anyhting about the convergence of the series.

Answer 1

1) a_n+1/a_n = [(n+1)^3+1]/n^3 **1/2 ==>1/2 <1 convergent
2)= (2n+1)*(2n+2)/(n+1)(n+4) ==>4>1 divergent
3) = sqrt(n)/sqrt(n+1) ==>1 does not tell us anything but the series is divergent by other criteria
3/sqrt(n) > 3/n