Mathematics for Computer Science

Chapter 13 Sums and Asymptotics536

(a)How much is a Harvard degree worth today if the holder will work fornyears
following graduation?

(b)How much is an MIT degree worth in this case?

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

Problem 13.5.
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 13.2

Class Problems

Problem 13.6.
Find a closed form for each of the following sums:
(a)
Xn

iD 1



1

iC 2012

1

iC 2013



:

(b)Assuming the following sum equals a polynomial inn, find the polynomial.
Then verify by induction that the sum equals the polynomial you find.

Xn

iD 1

i^3

Problems for Section 13.3

Practice Problems

Problem 13.7.
Let

SWWD

X^5

nD 1

p

3n: