Answer:
Step-by-step explanation:
Hello, we want to prove that a proposition depending on n, that we can note P(n), is true for any n positive integer greater than 1. We need to follow several steps.
Step 1 - prove P(1)
For n = 1, n(2n+1)=1*3 =3 so we have
3 = 3, which is obviously true.
First step done!
Step 2 - for we assume P(k) and we need to prove P(k+1)
We assume that 3+7+11+...+(4k-1)=k(2k+1)
so we can write that
3+7+11+...+(4k-1)+(4(k+1)-1)=k(2k+1)+(4k+4-1)=k(2k+1)+4k+3
and
(k+1)(2(k+1)+1)=(k+1)(2k+3)
These two expressions are the same so it means that P(k+1) is true, meaning that
3+7+11+...+(4k-1)+(4(k+1)-1)=(k+1)(2(k+1)+1)
Step 3 - The conclusion
Finally, we have just proved that
3+7+11+...+(4n-1)=n(2n+1) for any n positive integer > 0
Thank you
Answer:
(6 / n) + 2
Step-by-step explanation:
<u>Step 1: Turn words into an algebraic expression</u>
two more than the quotient of six and a number, n
(6 / n) + 2
Answer: (6 / n) + 2
Answer: Jessica wants 120 plants in her garden.
Explanation:
Lets find the area of the triangle first:
Tip: the formula can be base x height divided by 2 so you cant get confised about 1/2bh.
Any side of the triangle can be a base, once u find a base, there will always be one corresponding height.
In this case, the base is 12 feet
And the height is 5 feet because that side is perpendicular/corresponding to the base, meaning that the side connects to the base in a 90 degree angle.
So we have this:
12 x 5/2 = 30
The area of the triangle is 30 square feet.
Now, if Jessica wants 4 plants for each square foot of area, we do this:
4 x 30 = 120
Co.mment me if u have any questions
MARK BRAINLIEST PLS TY
Im pretty sure it’s the last one.