A Series of Even numbers squared

In summary, a series of even numbers squared is a sequence of numbers obtained by multiplying each even number by itself. It is different from a regular series of even numbers because it only includes even numbers that have been squared. The pattern in this series is that each number is the square of the previous even number with a difference of 4. This series is significant in mathematics for calculations and demonstrating patterns. It can also include negative numbers in its sequence.
  • #1
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Homework Statement



Is there a general formula for the sum of such a series (or can it be self derived) ?

2^2 + 4^2 + 6^2 + 8^2 ... N^2 (all the way till some even number N)

Homework Equations



[itex]\sum r^2[/itex] (from r=1 to r=N) = 1/6 * n(n+1)(2n+1)

The Attempt at a Solution



No clue where to start.
 
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  • #2
Do all the terms have a common factor that you can pull out?
 
  • #3
Oh... I did not see that. Great thinking !

After taking 2^2 common we will get a simple sequence :

1^2 + 2^2 + 3^2 + 4^2 ...

I think I get it !
 

Related to A Series of Even numbers squared

1. What is a series of even numbers squared?

A series of even numbers squared is a sequence of numbers that are obtained by multiplying each even number by itself (squaring it). For example, the first few numbers in this series are 4, 16, 36, 64, and so on.

2. How is a series of even numbers squared different from a regular series of even numbers?

A regular series of even numbers includes all even numbers in a consecutive sequence, while a series of even numbers squared includes only the even numbers that have been multiplied by themselves.

3. What is the pattern in a series of even numbers squared?

The pattern in a series of even numbers squared is that each number in the series is the square of the previous even number, with a difference of 4 between each number. For example, 4 is the square of 2, 16 is the square of 4, 36 is the square of 6, and so on.

4. What is the significance of a series of even numbers squared in mathematics?

A series of even numbers squared is often used in mathematical calculations and equations. It is also used to demonstrate patterns and relationships between numbers, and can be helpful in understanding concepts such as exponents and square roots.

5. Can a series of even numbers squared include negative numbers?

Yes, a series of even numbers squared can include negative numbers. In this case, the sequence would include both positive and negative even numbers, such as -4, 4, -16, 16, -36, 36, and so on.

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