Exam 8: Extension B: Infinte Sequences and Series

Determine whether the series is convergent or divergent by expressing as a telescoping sum.If it is convergent,find its sum.

Determine whether the series is convergent or divergent by expressing as a telescoping sum.If it is convergent,find its sum.

Determine whether the geometric series converges or diverges.If it converges,find its sum.

A sequenceis defined recursively by the equation for where Use your calculator to guess the limit of the sequence.

Express the number as a rational number.

Determine whether the given series converges or diverges.If it converges,find its sum.

When money is spent on goods and services,those that receive the money also spend some of it.The people receiving some of the twice-spent money will spend some of that,and so on.Economists call this chain reaction the multiplier effect.In a hypothetical isolated community,the local government begins the process by spending D dollars.Suppose that each recipient of spent money spends and saves of the money that he or she receives.The values c and s are called the marginal propensity to consume and the marginal propensity to save and,of course, The number k = 1/s is called the multiplier.What is the multiplier if the marginal propensity to consume is ?

Determine whether the given series converges or diverges.If it converges,find its sum.

Determine whether the given series converges or diverges.If it converges,find its sum.

A right triangle ABC is given with and CD is drawn perpendicular to AB,DE is drawn perpendicular to BC,EF AB and this process is continued indefinitely as shown in the figure.Find the total length of all the perpendiculars Write your answer to two decimal places.

Express the number as a ratio of integers.