Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 3 + 
+ 
+ . . . + 
= 4
What will be an ideal response?
| S1: | 3  4 |
4
3 = 3 ?
Sk: 3 +
+ 
+ . . . + 
= 4
Sk+1: 3 +
+ 
+ . . . + 
= 4
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
to both sides.3 +
+ 
+ . . . + 
+ 
= 4
+ 
3 +
+ 
+ . . . + 
= 4 - 
+ 
3 +
+ 
+ . . . + 
= 
3 +
+ 
+ . . . + 
= 
3 +
+ 
+ . . . + 
= 
- 
3 +
+ 
+ . . . + 
= 4 - 
3 +
+ 
+ . . . + 
= 4
We have shown that if we assume that Sk is true, and we add
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...
Evaluate the spherical coordinate integral.
A. 
?
B. 
?
C. 
?
D. 
?
Mathematics
Find the integral.
dx
A. sec x + C B. csc x + C C. -sec x + C D. -csc x + C
Mathematics
Calculate. Round to two decimal places if necessary.
A. 138.56 B. 6.32 C. 5.54 D. 208.44
Mathematics
For which type of mathematics problem is the "odometer strategy" commonly used by students?
a. Fundamental Counting Principle problems b. Fundamental Theorem of Arithmetic problems c. Vector addition problems d. Matrix multiplication problems
Mathematics