Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6n = 
What will be an ideal response?
| S1: | 1 ? 6   |
6 = 6 ?
Sk: 1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6k =
Sk+1: 1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6(k + 1) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
6(k+1), to both sides."
1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6k + 6(k + 1) =
+ 6(k + 1)1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6(k + 1) =
+ 
1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6(k + 1) =
1 ? 6 + 2 ? 6 + 3 ? 6 + . . . + 6(k + 1) =
We have shown that if we assume that Sk is true, and we add (6(k+1) to both sides of Sk , then Sk+1 is also true. By the principle of mathematical induction, the statement Sn is true for every positive integer n.
Mathematics
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A. 1.99 B. 2.77 C. -1.20 D. 1.58
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Construct a truth table for the statement.~q ? (~p ? q)
A. 
| T | T | F | F | F | F |
F T T F F T
F F T T T T
B.
| T | T | F | F | T | T |
F T T F F F
F F T T T T
C.
| T | T | F | F | F | F |
F T T F F T
F F T T T T
D.
| T | T | F | F | T | T |
F T T F T T
F F T T T T
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Give the rectangular coordinates for the point.(4, 45°)
A. (2
, 2
)
B. (-2
, -2)
C. (2
, 2)
D. (-2, -2
)
Mathematics
Translate the phrase into a mathematical expression. Use x to represent "a number". The quotient of a number and 4
A. x - 4
B. 
C. 4x
D. 
Mathematics