Use mathematical induction to prove that the statement is true for every positive integer n.1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5n = 
What will be an ideal response?
| S1: | 1 ? 5   |
5 = 5 ?
Sk: 1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5k =
Sk+1: 1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5(k + 1) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
5(k+1), to both sides."
1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5k + 5(k + 1) =
+ 5(k + 1)1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5(k + 1) =
+ 
1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5(k + 1) =
1 ? 5 + 2 ? 5 + 3 ? 5 + . . . + 5(k + 1) =
We have shown that if we assume that Sk is true, and we add (5(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. f(x) = 
- 
+ 
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B. f(x) = 
- 
+ 
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C. f(x) = 
+ 
+ 
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D. f(x) = 
- 
+ 
(3 sin x - sin 2x + . . .)
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A. 
B. 
C. 
D. 
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Number of Hours Spent Traveling
A. 0.2 mph B. 5.2 mph C. 3.2 mph D. 0.3 mph
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A. 70.8° B. 73.1° C. 72° D. 71.3° E. 72.3°
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