Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 1 + 
+ 
+ . . . + 
= 2
What will be an ideal response?
| S1: | 1  2 |
2
1 = 1 ?
Sk: 1 +
+ 
+ . . . + 
= 2
Sk+1: 1 +
+ 
+ . . . + 
= 2
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
to both sides.1 +
+ 
+ . . . + 
+ 
= 2
+ 
1 +
+ 
+ . . . + 
= 2 - 
+ 
1 +
+ 
+ . . . + 
= 
1 +
+ 
+ . . . + 
= 
1 +
+ 
+ . . . + 
= 
- 
1 +
+ 
+ . . . + 
= 2 - 
1 +
+ 
+ . . . + 
= 2
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.You might also like to view...
Convert between English and Metric System of Units.
2.5 m = 
in. (Round to the nearest tenth.)
A. 98.4 B. 6.4 C. 2.7 D. 90.0
Solve the following system by any appropriate method. If there is no real number solution, so state.3x2 - y2 = 14x2 + 2y2 = 14
A. (
, 2), (
, -2), (-
, 2), (-
, -2)
B. (
, 4), (
, -4), (-
, 4), (-
, -4)
C. (
, 2), (
, -2), (-
, 2), (-
, -2)
D. no real solution
Find the exact value, given that sin A = -4/5 with A in quadrant IV, 
with B in quadrant III, and 
with C in quadrant II.tan 2B
A. 
B. - 
C. 
D. - 
Solve.A city government budgeted $31.3 million for public transportation. This was $14.9 million more than was budgeted for parks and recreation. Solve the equation 
to find how much was budgeted for parks and recreation.
A. $15.9 million B. $16.4 million C. $20.4 million D. $17.4 million