

Due date if any

Fuchsia means graded homework.



1214 February


Section 2.5: 8a.

Section 2.5: 2, 5a, 6.



59 February


Section 2.5: 1.

Section 2.4: 5a, 8.

Section 2.4: 2cd, 4ab, 6.

Section 2.3: 19a, 20abc, 21.



292 Jan/February


Section 2.3: 4b, 12, 14, 18.

Section 2.3: 2, 6.

Section 2.2: 2, 4.

Section 2.1: 1, 2, 10.



2226 January


Convert the decimal number 99 into binary.
Convert the binary number 10101 into decimal.

When we expand (a+b)^13, what is the (binomial) coefficient in front of
a^9*b^4?
Write your final answer as a decimal number.

Section 1.2: 1, 8.

Think of a good more general formula than the one in Section 1.2.2.
Then try to prove this more general formula to be correct.

Consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by

a_n = 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(n*(n+1)).

By trial and experiment find a `closed' simple expression for a_n.

Prove by induction on n that this `closed' simple expression for a_n is always
correct.

Section 1.2: 2, 3.



1719 January


Section 1.1: 8.
Also, compute 12! (twelve factorial).
Also, consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by

a_1 = 1, and for all n >= 2 we have a_n = a_1 + a_2 + a_3 + ... + a_(n1).

By trial and experiment find a `closed' simple expression for a_n.

Prove by induction on n that this `closed' simple expression for a_n is always
correct.

Section 1.1: 1ae, 2, 9.
