Use induction to prove that 2? ? ? for any integer n> 0 . indicate type of induction used.
i proved the base case using n = 1, and for my induction hypothesis, i said that we assume n = k for 2^k > k, but i am stuck trying to get to n = k + 1.
so far i have:
2^k > k
2*2^k > 2*k
2^{k+1} > 2k

Answer with explanation:

The given statement is which we have to prove by the principal of Mathematical Induction

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

                   ---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement  is true for, n=k+1.

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

1/4 because there is 4 grades.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: