Determine if the statements are true Determine if the following statements are t

Question

Determine if the statements are true

Determine if the following statements are true or false. a) If 0 ansbn and an converges, then bn converges. True False b) If OsanS bn and an diverges, then bn diverges. b) If 0 an bn and an diverges, then bn diverges. True False . c) If-an converges, then l anl Converges True False d) If Ian + bnl converges, then lanl converges and 1bnl converges. True False an converges. e) If the terms, an, of a series approach zero as n approaches infinity, then the series True False

Explanation / Answer

1) The first answer is False, since bn is a upper bound then an hence convergence of an doesn't assure us that bn series will also converge

2) The second answer is True, since bn is a upper bound then if bn converges then an will surely converge

3) The third answer is false, since it is not necessary that an converges implies to |an| converges but vice versa is true i,e, if modulus of series converges then the series will converge

4) The fourth answer is false, considering an = n^2 (not converging) and bn = -n^2 (not convering) in this case |an+bn| will converge but |an| and |bn| doesn't converge

5) The fifth statement is true according to the ratio test

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