5–40 determine whether each integral is convergent or divergent. evaluate those that are convergent. 20

Determine whether  the  geometric series.  ∞. ∑  n=1  en. 3n−1  is  convergent  or  divergent. if it isconvergent, find its sum. answer: i can re-write the terms as en. 3n−1  (  n n  +  1. ) = lim  n→∞  sn = limn→∞. (−ln(n  +  1)) =  −∞, so the given series diverges. 48. find the values of x for which the series.  ∞. ∑n=1. (x  − 4)n converges.