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 
.
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Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.s = -cot 4t
A. Period ?, symmetric about the origin
B. Period 
, symmetric about the origin
C. Period 
, symmetric about the s-axis
D. Period 
, symmetric about the origin
Solve the problem.The accompanying figure shows the graph of y = x2 shifted to a new position. Write the equation for the new graph.
A. y = x2 + 6 B. y = (x + 6)2 C. y = x2 - 6 D. y = (x - 6)2
Solve the logarithmic equation.ln x - ln (x - 6) = ln 8
A. 2
B. 
C. 
D. No solution
Find the amount of decrease and the percent decrease.
A. 
B. 
C. 
D. 