Question

Exercise 5.12. Determine whether the infinite series is convergent, of vergent. Show your reasoning. In particular, make clear which of the several available tests you are using. X 0 ΣΠΗ3 ο Στη + 1)(n + 3) 4) Στ+6 η2 + 5η +6

please do a,b,c,d, j, k ,m ,r,s

Answer 1

a) This series is divergent by Limit Comparison Test.Compare this series with the series 1/n.

b) This series is convergent by Limit Comparison Test. Compare this series with the series 1/n^(3/2).

c) This series is convergent by Limit Comparison Test. Compare this series with the series 1/n^2.

d) This series is divergent by Limit Comparison Test. Compare this series with the series 1/n.

j) This series is convergent by Comaprison Test. Since |sin(n^2)| is less equal one and Comaparing with the series 1/n^2.

k) This series is convergent because it is geometric series.We can replace here 3^(n/2) by 3^n

m) This is divergent series by Limit Comparison Test.Compare this This series with the series 1/n

r) This is divergent series by nth Term Test. S