00:01
So, it is given to us that 2 to the power 0 plus 2 to the power 1 plus 2 to the power 2 plus 2 to the power 3 and so on till 2 to the power n is equals to 2 to the power n plus 1 minus 1 for any non -negative integer.
00:26
So, we will let this as equation a.
00:30
Now, using the induction proof, induction proof, so rhs will be n is equals to 1, 2 to the power 1 plus 1 minus 1 will be equal to 4 minus 1 which is equals to 3.
00:56
Now, we will solve lhs, we will keep the value of n as 1 only and 2 to the power 0 plus 2 to the power 1 is equals to 1 plus 2 which is equals to 3.
01:13
Therefore, we can say lhs is equals to rhs.
01:18
Now, let us consider the given equation.
01:21
Now, let us consider the given equation is true for n is equals to k...