Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Show that the formula 
obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for some natural number k, it is also true for the next natural number 
. Then show that the formula is false for 
.
What will be an ideal response?
Assume the statement is true for some natural number k. Then
So the statement is true for 
.
However, when 
, the left side of the statement is 
, and the right side of the statement is 
, so the formula is false for 
.
Mathematics
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Find the domain of the function. Put your answer in set-builder notation.f(x) = 
A. {x 
B. {x 
C. {x 
D. {x 
Mathematics
Solve.
2 - 8 
+ 15 = 0
A. 
, 
B. ±
, ±
C. ±
, ±
D. ±
Mathematics
Simplify the trigonometric expression by following the indicated direction.Factor and simplify: 
What will be an ideal response?
Mathematics
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
A. 
B. 
C. 
D. 1
Mathematics