91Ó°ÊÓ

Using the big-oh notation, estimate the growth of each function. $$f(n)=\lg (5 n) !$$

Find the set of possible remainders when an integer is divided by the given integer. Two

Suppose you sent your love 1 gift on the first day of Christmas, \(1+2\) gifts on the second day, \(1+2+3\) gifts on the third day and so on. $$\sum_{i=1}^{n} i^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$$

Express each decimal number as required. $$1776=(\quad)_{\text {eight }}$$

Algorithm 4.13 finds the maximum value in a list \(X\) of \(n\) items. Use it to answer Exercises. Algorithm find max \((X, n, \max )\) (* This algorithm returns the largest item in a list \(x\) of \(n\) items in a variable called max. *) 0\. Begin (* algorithm *) 1\. \(\max \leftarrow x_{1}\) (* initialize max *) 2\. \(i \leftarrow 2\) 3\. while \(1 \leq n \mathrm{do}\) 4\. begin (* while *) 5\. if \(x_{1}>\) nax then (*update max *) 6\. \(\max \leftarrow x_{1}\) 7\. \(i \leftarrow i+1\) 8\. end while 9\. End (*algorithm *) Establish the correctness of the algorithm.

Using the big-oh notation, estimate the growth of each function. $$f(n)=23$$

Find the set of possible remainders when an integer is divided by the given integer. Five

(Twelve Days of Christmas) Suppose you sent your love 1 gift on the first day of Christmas, \(1+2\) gifts on the second day, \(1+2+3\) gifts on the third day and so on. $$ \sum_{i=1}^{n} a r^{i-1}=\frac{a\left(r^{n}-1\right)}{r-1}(r \neq 1) $$

Using the euclidean algorithm, find the gcd of the given integers. $$2076,1776$$

Express each decimal number as required. $$2076=(\quad)_{\text {sixteen }}$$