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Why is the sum of consecutive odd numbers always the difference of two squares?
Wiki User
∙ 14y ago
Because the sum of the first N odd numbers is always N squared. Look at 5, 7, and 9. This is 5+7+9 = (1 + 3 + 5 + 7 + 9)-(1+3)= 25-4 =5^2 - 2^2
Wiki User
∙ 14y ago
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What is the difference of two consecutive odd numbers after 235?
The difference of two consecutive odd numbers is always two. Whether it is before 235 or after is irrelevant.
Does the difference of two squares number always factorable?
No. If the two numbers are consecutive then the difference of their squares need not be factorisable. For example, 4^3 - 3^3 = 16 - 9 = 7, which is a prime. If the smaller number is a then this simply requires that 2a+1 is a prime.
What is the difference between the two odd numbers right after 20?
The difference is 2. (23 - 21 = 2).If we are talking about two odd numbers that come right after the number 20 then we mean the two consecutive odd numbers after 20.The difference between any consecutive odd numbers (or between any consecutive even numbers) is always 2.
What is the difference between two consecutive odd numbers?
The different between two different odd numbers are always an even number
In which quadrilaterals are consecutive angles always congruent?
Only in squares and rectangles. In a rhombus, the consecutive angle is supplementary (sums to 180 degrees).
What is the difference of two consecutive odd numbers after 235?
The difference of two consecutive odd numbers is always two. Whether it is before 235 or after is irrelevant.
Does the difference of two squares number always factorable?
No. If the two numbers are consecutive then the difference of their squares need not be factorisable. For example, 4^3 - 3^3 = 16 - 9 = 7, which is a prime. If the smaller number is a then this simply requires that 2a+1 is a prime.
What is the difference between the two odd numbers right after 20?
The difference is 2. (23 - 21 = 2).If we are talking about two odd numbers that come right after the number 20 then we mean the two consecutive odd numbers after 20.The difference between any consecutive odd numbers (or between any consecutive even numbers) is always 2.
What is the difference between two consecutive odd numbers?
The different between two different odd numbers are always an even number
Why can't two consecutive whole numbers be prime?
In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.
Why 35 and 7 are the only three consecutive odd prime numbers?
If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.
Which quadrilateral are consecutive angles always congruent?
All rectangles, including squares.
How do you make 92 with consecutive numbers?
Adding consecutive pairs of numbers will always turn out to be an odd number. It would have to be consecutive odd numbers: 45 and 47.
Is the sum of two consecutive numbers always divisible by 2?
No, the sum of two consecutive numbers is always an odd number, and is not divisible by two.
If you square two consecutive whole numbers and substract from the larger Is it possible that the difference is an even number?
No. The difference between the squares of two successive integers is always an odd number, the sum of your two original numbers eg 42 - 32 = 16 - 9 = 7 = 4 + 3. Another example 472 - 462 = 2209 - 2116 = 93 = 47 + 46. The proof is straightforward, based on the squares of n and n - 1...
In which quadrilaterals are consecutive and oppositive angles always congruent?
All rectangles (this includes squares).
In which quadrilaterals are consecutive angles always congruent?
Only in squares and rectangles. In a rhombus, the consecutive angle is supplementary (sums to 180 degrees).
