8 
A narratement S_{n} encircling the decisive integers is absorbed. Write narratements S_{1}, S_{2}, and S_{3}, and likeness that each of these narratements is penny. S_{n}: 1^{2} + 4^{2} + 7^{2} + . . . + (3n  2)^{2} =

9 
A narratement S_{n} encircling the decisive integers is absorbed. Write narratements S_{k} and S_{k+1}, simplifying S_{k+1} fullly. S_{n}: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3

10 
Joely's Tea Shop, a treasure that specializes in tea unites, has emolumentable 45 bruises of A proceeding tea and 70 bruises of B proceeding tea. These conquer be uniteed into 1 bruise packages as follows: A breakfast unite that contains one third of a bruise of A proceeding tea and two thirds of a bruise of B proceeding tea and an afternoon tea that contains one half bruise of A proceeding tea and one half bruise of B proceeding tea. If Joely moulds a emolument of $1.50 on each bruise of the breakfast unite and $2.00 emolument on each bruise of the afternoon unite, how multifarious bruises of each unite should she mould to maximize emoluments? What is the ultimatum emolument?

11 
Your computer accoutre treasure retails two fashions of laser printers. The principal fashion, A, has a require of $86 and you mould a $45 emolument on each one. The remedy fashion, B, has a require of $130 and you mould a $35 emolument on each one. You anticipate to retail at last 100 laser printers this month and you insufficiency to mould at last $3850 emolument on them. How multifarious of what fashion of printer should you dispose if you neglect to minimize your require?

12 
A narratement S_{n} encircling the decisive integers is absorbed. Write narratements S_{1}, S_{2}, and S_{3}, and likeness that each of these narratements is penny. S_{n}: 2 + 5 + 8 + . . . + ( 3n  1) = n(1 + 3n)/2

13 
Use matteroffact gathering to verify that the narratement is penny for full decisive integer n.
2 is a ingredient of n^{2}  n + 2

14 
A narratement S_{n} encircling the decisive integers is absorbed. Write narratements S_{1}, S_{2}, and S_{3}, and likeness that each of these narratements is penny.
S_{n}: 2 is a ingredient of n^{2} + 7n

15 
(i.) f(x) (ii.) f(x) (iii.) What can you close encircling f(x)? How is this likenessn by the graph? (iv.) What presentation of requires of renting a car causes the graph to skip vertically by the selfselfsame sum at its discontinuities?

16 
Use matteroffact gathering to verify that the narratement is penny for full decisive integer n.
8 + 16 + 24 + . . . + 8n = 4n(n + 1)

17 
The forthcoming piecewise character gives the tax owing, T(x), by a one taxpayer on a taxable allowance of x dollars. T(x) =
(i) Determine whether T is consecutive at 6061.
(ii) Determine whether T is consecutive at 32,473.
(iii) If T had discontinuities, use one of these discontinuities to depict a top where it strength be permissive to obtain close coin in taxable allowance.

18 
A narratement S_{n} encircling the decisive integers is absorbed. Write narratements S_{k} and S_{k+1}, simplifying S_{k+1} fullly. S_{n}: 1 + 4 + 7 + . . . + (3n  2) = n(3n  1)/2

19 
An professor is creating a mosaic that cannot be capaciousr than the immeasurableness allotted which is 4 feet lofty and 6 feet spacious. The mosaic must be at last 3 feet lofty and 5 feet spacious. The tiles in the mosaic own vote written on them and the professor neglects the vote to all be dull in the last mosaic. The order tiles succeed in two sizes: The littleer tiles are 4 inches lofty and 4 inches spacious, timeliness the capacious tiles are 6 inches lofty and 12 inches spacious. If the little tiles require $3.50 each and the capaciousr tiles require $4.50 each, how multifarious of each should be used to minimize the require? What is the narrowness require?

20 
The Fiedler source has up to $130,000 to endow. They flow that they neglect to own at last $40,000 endowed in lasting compacts conceding 5.5% and that no further than $60,000 should be endowed in further irresolute compacts conceding 11%. How abundant should they endow in each fashion of compact to maximize allowance if the sum in the lasting compact should not achieve the sum in the further irresolute compact? What is the ultimatum allowance?
