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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Simplify the expression. Assume all variables represent positive real numbers.
A. 9 B. 5 C. ±3 D. 3
Mathematics
Factor.4x2 + 12x + 9
A. (2x + 3)(2x - 3) B. (4x + 1)(x + 9) C. (2x + 3)2 D. (2x - 3)2
Mathematics
Use the method of matrix inverses to solve the system.
A. (10, -5, -5) B. (12, -4, -4) C. (12, -6, -6) D. (11, -5, -5) E. (10, -4, -4)
Mathematics
Write the number in simplest form, without a negative radicand.
A. 3i
B. i
C. -3i
D. 5i
Mathematics