Use mathematical induction to prove that the statement is true for every positive integer n.2 + 5 + 8 + . . . + (3n - 1) = 
What will be an ideal response?
| S1: | 2   |
2 = 2 ?
Sk: 2 + 5 + 8 + . . . + (3k - 1) =
Sk+1: 2 + 5 + 8 + . . . + (3k + 2) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
3(k+1) - 1, to both sides.
2 + 5 + 8 + . . . + (3k - 1) + (3(k + 1) - 1) =
+ (3(k + 1) - 1)2 + 5 + 8 + . . . + (3k + 2) =
+ (3k + 2)2 + 5 + 8 + . . . + (3k + 2) =
+ 
2 + 5 + 8 + . . . + (3k + 2) =
2 + 5 + 8 + . . . + (3k + 2) =
We have shown that if we assume that Sk is true, and we add 3(k+1) - 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
You might also like to view...
An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods.(6, 6)
A. 45°; N 45° E B. 45°; S 45° E C. 45°; S 45° W D. 45°; N 45° W
Mathematics
Solve the equation.|6x - 6| + 6 = 12
A. 
B. 
C. ?
D. 
Mathematics
Evaluate the function for the indicated value.h(x) = 
; find h(19)
A. 4 B. -34 C. -4 D. 34
Mathematics
Solve the system of two equations in two variables.-6x + 66 = 6y 3x - 3y = 15
A. (7, 4) B. (8, 4) C. No solution D. (8, 3)
Mathematics