Mathematics for Computer Science

Chapter 14 Sums and Asymptotics438

(c)If you plan to retire after twenty years, which degree would be worth more?

Problem 14.4.
Suppose you deposit $100 into your MIT Credit Union account today, $99 in one
month from now, $98 in two months from now, and so on. Given that the interest
rate is constantly 0.3% per month, how long will it take to save $5,000?

Problems for Section 14.3

Exam Problems

Problem 14.5.
Assumenis an integer larger than 1. Circle all the correct inequalities below.
Explanations are not required, but partial credit for wrong answers will not be
given without them.Hint:You may find the graphs in Figure 14.11 helpful.



Xn

iD 1

ln.iC1/ln 2 C

Zn

1

ln.xC1/dx



Xn

iD 1

ln.iC1/

Zn

0

ln.xC2/dx



Xn

iD 1

1

i



Zn

0

1

xC 1

dx

Homework Problems

Problem 14.6.
Letf WRC!RCbe a weakly decreasing function. Define

SWWD

Xn

iD 1

f.i/

and

IWWD

Zn

1

f.x/dx:

Prove that
ICf.n/SICf.1/:
Hint:See Theorem 14.6.