By the definition above,
and by substitution we get
If we keep following this procedure, we'll start to see a pattern:
and so on, down to
Now,
One of these series is geometric and has a well-known closed form:
The other (see note below) is a bit less obvious, but can be derived:
so we have
# # #
A brief note on how to compute the sum,
The first term of the sum is 0:
Add and substract 1 to the first factor in the summand and expand the sum into two sums:
The latter sum we're familiar with. For the other sum, we can shift the index to make it start at , and again the first term in the sum would be 0:
So we have
Continuing in this way, we would end up getting
or as a double sum,
which is easy to reduce:
Answer:
$13500
Step-by-step explanation:
Given
Each tile cover one ninth of a square yard and each tile costs $3
First, area of the Swimming Pool(from the diagram)
=Area of Left rectangle(length=20,breadth=10)+ Area of Square in middle(side=10)+Area of right rectangle(length=20,breadth=10)
We have to calculate how many tiles make up 500 yards
As given each tile is one ninth of a yard
⇒Number of tiles that make up 500 yards, n
⇒ As each tile costs $3
Therefore total cost to tile the floor
Therefore total cost of tiles=$13500
3. -3. 6. -9
10. 2 = AB 0. 15 =3A
10. -1. 21. -6
Answer: mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.
Step-by-step explanation:here a clue have a wonderful Christmas break ❄️
D.15 because 15 divided by 5 is 3 and 3+7 is equal to 10. Hope that helped