please answer both questions from your own work on a paper providing all steps for good feedback.

1. For each sequence below, answer the following questions. As always, explain your reasoning. {4 5 6 T } {2 3 4 5 } 1' 2' 3' 4' 3' 9' 2?' 81' a) What is the limit of the sequence [if it has one]? b] ls the sequence convergent? c] ls the sequence monotonic? d] ls the sequence bounded? e) What is its dening equation [if it has one]? 2. A series is called geomem'c if each term is generated by multiplying the preceding term by a common ratio. The general form for a geometric series is on Zorni=a+ar+nr2+ar3+m n=1 Use the following steps to learn about the general behavior ofan innite geometric series. a) For what values of r is the sequence {rn} convergent? b) Write an equation to express 1 + r + r2 + r3 + + r\"1 as a fraction. (Hint: Try multiplying it by 1 1'.) Then write limit notation as n > no in front of both sides of this equation. c] For what values of r is the limit on the right side of the equation dened and nite? d) Explain whyr a geometric series [as expressed above] is convergent when |r| <: and divergent when e show that every convergent innite geometric series has a sum equal to of r t find the ofthe>