Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.
The constant should be added to form a perfect square trinomial will be 1/4. Then the correct option is D.
<h3>What is a quadratic equation?</h3>It's a polynomial with a value of zero. There exist polynomials of variable power 2, 1, and 0 terms. A quadratic equation is an equation with one statement in which the degree of the parameter is a maximum of 2.
The expression is x² + x.
Then the constant should be added to form a perfect square trinomial.
Then the constant will be
The square of the half of the coefficient of the variable x is to be added to make a perfect square.
Then the constant will be 1/4.
Then the perfect square will be
More about the quadratic equation link is given below.
#SPJ1