CSC252a
Fall 2000
Ileana Streinu

Informal Homework 0

This is just to help you recapitulate some formulas and limit calculations.

Limits

Compute the limit of the following function ratios, as n goes to infinity:

1.	(2n^2 + 3n-5)/(5n^2-3n+1)
2.	(2n)/(3n)
3.	(n^n)/(2^(n log n))
4.	(n^2 + 2^n)/((1.5)^n)
5.	(n!)/(n^n)

Formulas

Find a closed formula for the following summations:

1.	1+2+ ... + n =
2.	1 + 2^2 + ... + n^2 =
3.	1 + 2 + 2^2 + ... + 2^n =
4.	1 + 3 + 3^2 + ... + 3^n =
5.	1 + x + x^2 + ... + x^n =

Last modified Sept. 12, 2000.