Quiz 6 will be on Friday, October 17.
You may use a scientific calculator, but not a graphing
or programmable calculator.

Remember, there are two versions of each quiz.

Problem 1: A geometric series.

Problem 2: A telescoping series.

Problem 3: An integral from 7.2 or 7.3.

Problem 4: (a) State the formal definition of the (finite) limit
           of a sequence.
           (b) Prove the first Limit Law (page 696: proof was 
           done in class, but see below.)


Theorem: Let {an} and {bn} be convergent sequences with limits L and K, respectively.
Then {an+bn} converges to L+K.

Proof: Let e > 0 be given.  

By the definition of a limit the exists an number N1 such that
if n > N1 then |an - L| < e/2.

By the definition of a limit the exists an number N2 such that
if n > N2 then |bn - K| < e/2.

Let N equal the bigger of N1 and  N2.

Now, for all n > N, we have,

|(an+bn) - (L+K)| = |(an-L) + (bn-K)| <= |an-L| + |bn-K| < e/2 + e/2 = e.

Thus, by the definition of a limit, an+bn --> L+K. QED


Rather than trying to memorize this, try to understand it, and then 
rewrite it in your own words.