A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Sn: 12 + 42 + 72 + . . . + (3n – 2)2 =
S₁=0(6(0)^2-3(0)-1)/2=(3(1)-2)^2=1 S₂=1(6(1)^2-3(1)-1)/2=4^2=16 S₃=2(6(2)^2-3(2)-1)/2=7^2=49
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A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
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Joely’s Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit?
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Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?
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A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Sn: 2 + 5 + 8 + . . . + ( 3n – 1) = n(1 + 3n)/2
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Use mathematical induction to prove that the statement is true for every positive integer n.
2 is a factor of n2 – n + 2
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A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true.
Sn: 2 is a factor of n2 + 7n
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