W07 Regular

Due date: Sunday 3/8, 11:59pm

Sequences

01

03

Computing the terms of a sequence

Calculate the first four terms of each sequence from the given general term, starting at :

(a) (b) (c) (d) (e) (f)

Link to original

Solution

Solutions---0140-03

02

02

Squeeze theorem

Determine whether the sequence converges, and if it does, find its limit:

(a) (b)

(Hint for (b): Verify that .)

Link to original

Solution

Solutions---0140-02

Series

03

05

Series from its partial sums

Suppose we know that the partial sums of a series are given by the formula .

(a) Compute .

(b) Find a formula for the general term .

(c) Find the sum .

Link to original

Solution

Solutions---0150-05

04

06

Partial sums and total sum

Consider the series:

(a) Compute a formula for the partial sum by applying the “shift method” steps using the values in this series.

(b) By taking the limit of this formula as , find the value of the series.

(c) Find the same value of the series by computing and and plugging into .

Link to original

Solution

Solutions---0150-06