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The sum of any two successive triangular number is a square number.
The nth triangular number is n(n+1)/2 = (n2 +n)/2
The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2
Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2
This is easy to visualise. For example T3 + t4 = 42
[T3, the 3th triangular number represented by X,
t4, the 4th triangular number represented by x]
XXX_____x
XX_____xx
X_____xxx
_____xxxx
Bring them together and you have:
XXXx
XXxx
Xxxx
xxxx
The sum of any two successive triangular number is a square number.
The nth triangular number is n(n+1)/2 = (n2 +n)/2
The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2
Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2
This is easy to visualise. For example T3 + t4 = 42
[T3, the 3th triangular number represented by X,
t4, the 4th triangular number represented by x]
XXX_____x
XX_____xx
X_____xxx
_____xxxx
Bring them together and you have:
XXXx
XXxx
Xxxx
xxxx
The sum of any two successive triangular number is a square number.
The nth triangular number is n(n+1)/2 = (n2 +n)/2
The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2
Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2
This is easy to visualise. For example T3 + t4 = 42
[T3, the 3th triangular number represented by X,
t4, the 4th triangular number represented by x]
XXX_____x
XX_____xx
X_____xxx
_____xxxx
Bring them together and you have:
XXXx
XXxx
Xxxx
xxxx
The sum of any two successive triangular number is a square number.
The nth triangular number is n(n+1)/2 = (n2 +n)/2
The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2
Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2
This is easy to visualise. For example T3 + t4 = 42
[T3, the 3th triangular number represented by X,
t4, the 4th triangular number represented by x]
XXX_____x
XX_____xx
X_____xxx
_____xxxx
Bring them together and you have:
XXXx
XXxx
Xxxx
xxxx
Wiki User
∙ 11y ago
Wiki User
∙ 11y agoThe sum of any two successive triangular number is a square number.
The nth triangular number is n(n+1)/2 = (n2 +n)/2
The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2
Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2
This is easy to visualise. For example T3 + t4 = 42
[T3, the 3th triangular number represented by X,
t4, the 4th triangular number represented by x]
XXX_____x
XX_____xx
X_____xxx
_____xxxx
Bring them together and you have:
XXXx
XXxx
Xxxx
xxxx
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What are the real numbers that is not a whole number?
Real numbers are all numbers which do not contain "i", when "i" represents the square root of -1. All numbers which do contain "i" are "imaginary numbers" and are not real numbers. This means that all numbers you'd ordinarily use are real numbers - all the counting numbers (integers) and all decimals are real numbers. So in answer to your question, all the real numbers that are not whole numbers are all the decimal numbers - including irrational decimals such as pi.
How do you check if a number is a triangular number?
you need to use this formula: n(n+1) T=--------- 2 So number times (number + 1) divided by 2. If the number you get is the same number as n its a triangular number. if it isn't well it isn't a triangular number.
There are numbers from 1 to n. they have to be inverted as n to 1 . How many moves are required if only two consecutive numbers are stampled at a time?
There are (n2 - n) / 2 moves required.I am not aware that "stampled" is a word beyond a cross between stampede and trample, but I believe you wish to reverse the order of numbers from 1 to n where only two consecutive numbers can be swapped per step.This process will show a pattern of triangular numbers. For example:Let us suppose there are 3 numbers 1,2,3: To move the last (highest) number to the first place requires 2 steps. The second highest number is now in the last place. To move it to the second place requires 1 step. Finished. Total = 3 steps.Or:If there are 4 numbers, i.e. 1,2,3,4:3 steps + 2 steps + 1 step = 6 steps total. We know it is only 3 steps more than the last example because once we have moved the 4 to the first place we then simply have to do the above again (rearrange the 1,2,3, to 3,2,1).So you can see that the number of steps are all triangular numbers.A triangular number is calculated by n(n+1) / 2. So we can use this formula, but we need to alter it because the number of steps are for the previous triangular number. E.g. Where there are 4 numbers we have to do 1+2+3 steps to reorder it (see above).Therefore if we make our formula (n - 1) n / 2 = (n2 - n) / 2 then this will work.
What are similarities and differences between Mayan number system and Hindu Arabic number system?
Both make use of a zero symbol but Mayan numbers have 20 as a base whereas Hindu-Arabic numbers have 10 as a base.
Where can you use prime numbers?
In every math problem you can ever do you can use prime numbers. 1+3 Both prime numbers. Most numbers are not prime but prime numbers only become a broblem when you try to factor them like in simple algebra.
How to do square root?
You find the same two numbers that make the number, then you use one of those numbers for your square root.
Why do some clubs have square corner flags and other clubs have triangular flags?
Those who have triangular flags have won the FA cup. any one can use any shape of flag as long as you have a flag on top of corner pole - many clubs use Pennant style or Moon Flags to make them stand out you do not need to have won a cup or league competition
What do you use to do Origami?
You use only paper and your hands to fold it. You can use multiple pieces of paper, but it's not required. The paper used is mostly square, rectangular or triangular.
What number can you multiply to make 200?
The square root of 200 ≈ 14.14213562373. If you were to use rational numbers, you could multiply 100 by 2.
How many faces triangular pyramid?
There are five faces in a triangular pyramid. Gosh person, use your math book! Sorry you are wrong. It depends on the base if it is a square it has 5 surfaces if the base is a triangle it has 4 surfaces. So you must examine your pyramid carefully so as not to make a simple mistake.
Why is a number a perfect square?
you can multiply two whole numbers together to get that. if you use graph paper, you could make a perfect square. the area of that square is called a perfect square because you can make a perfect square using that many units as the area. for example 4x4=16, so 16 would be the perfect square.
What are the square numbers up to 1000?
They are the squares of the numbers 1 to 31. Use a calculator to find them.
How do you use the word triangular in a sentence?
The boat had triangular sails.
Where you use complex number?
Complex numbers are the square roots of negative numbers. i.e. root -1 = i
How do you use triangular in a sentence?
The boat was small and had two triangular sails.
Are hexagonal shapes strong?
They are. For all the material the use, you could make a really strong triangular pyramid.
What shape has 5 faces 8 edges and 8 vertices?
This describes a square pyramid. It has a square for a base, and four triangular sides that meet at the "top" or upper vertex. It will then have 5 faces, which will be the 4 triangular sides and the square base. It will also have 8 edges and 8 vertices. Use the link below to see a drawing and you can count all the faces, edges and vertices.
