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Sum of squares of first n even numbers Solution

STEP 0: Pre-Calculation Summary
Formula Used
sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3
Sne = (2*n*(n+1)*(2*n+1))/3
This formula uses 1 Variables
Variables Used
Value of n- Value of n is the index value of position n in a series or a sequence.
STEP 1: Convert Input(s) to Base Unit
Value of n: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Sne = (2*n*(n+1)*(2*n+1))/3 --> (2*3*(3+1)*(2*3+1))/3
Evaluating ... ...
Sne = 56
STEP 3: Convert Result to Output's Unit
56 --> No Conversion Required
FINAL ANSWER
56 <-- Sum of squares of first n even numbers
(Calculation completed in 00.001 seconds)

9 General Series Calculators

Sum of n natural numbers taken power of four
sum_of_n_natural_numbers_taken_power_of_4 = (Total terms*(Total terms+1)*((6*Total terms^3)+(9*Total terms^2)+Total terms-1))/30 Go
Sum of squares of first n even numbers
sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3 Go
Sum of Squares first n odd numbers
sum_of_square_of_first_n_odd_number = (Value of n*(2*Value of n+1)*(2*Value of n-1))/3 Go
Sum of squares of first n natural numbers
sum_of_first_n_terms = (Value of n*(Value of n+1)*(2*Value of n+1))/6 Go
Sum of cubes of first n natural numbers
sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4 Go
Sum of first n natural numbers
sum_of_first_n_terms = (Value of n*(Value of n+1))/2 Go
Sum of first n even natural numbers
sum_of_first_n_terms = (Value of n*(Value of n+1)) Go
Sum of cubes of first n even numbers
sum_required = 2*(Value of n*(Value of n+1))^2 Go
Sum of first n odd natural numbers
sum_of_first_n_terms = (Value of n)^2 Go

Sum of squares of first n even numbers Formula

sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3
Sne = (2*n*(n+1)*(2*n+1))/3

What is a even number?

The even numbers are the numbers which are divisible by 2. for example 2,4,6,8,10,12,14,16,18,20,22,24....etc

How to Calculate Sum of squares of first n even numbers?

Sum of squares of first n even numbers calculator uses sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3 to calculate the Sum of squares of first n even numbers, The Sum of squares of first n even numbers formula is defined as The sum of even numbers from 1 to infinity can be found easily, using Arithmetic Progression. As we know, the even numbers are the numbers which are divisible by 2. Sum of squares of first n even numbers and is denoted by Sne symbol.

How to calculate Sum of squares of first n even numbers using this online calculator? To use this online calculator for Sum of squares of first n even numbers, enter Value of n (n) and hit the calculate button. Here is how the Sum of squares of first n even numbers calculation can be explained with given input values -> 56 = (2*3*(3+1)*(2*3+1))/3.

FAQ

What is Sum of squares of first n even numbers?
The Sum of squares of first n even numbers formula is defined as The sum of even numbers from 1 to infinity can be found easily, using Arithmetic Progression. As we know, the even numbers are the numbers which are divisible by 2 and is represented as Sne = (2*n*(n+1)*(2*n+1))/3 or sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3. Value of n is the index value of position n in a series or a sequence.
How to calculate Sum of squares of first n even numbers?
The Sum of squares of first n even numbers formula is defined as The sum of even numbers from 1 to infinity can be found easily, using Arithmetic Progression. As we know, the even numbers are the numbers which are divisible by 2 is calculated using sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3. To calculate Sum of squares of first n even numbers, you need Value of n (n). With our tool, you need to enter the respective value for Value of n and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Sum of squares of first n even numbers?
In this formula, Sum of squares of first n even numbers uses Value of n. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • sum_of_first_n_terms = (Value of n*(Value of n+1))
  • sum_of_first_n_terms = (Value of n)^2
  • sum_of_square_of_first_n_even_number = (2*Value of n*(Value of n+1)*(2*Value of n+1))/3
  • sum_required = 2*(Value of n*(Value of n+1))^2
  • sum_of_n_natural_numbers_taken_power_of_4 = (Total terms*(Total terms+1)*((6*Total terms^3)+(9*Total terms^2)+Total terms-1))/30
  • sum_of_square_of_first_n_odd_number = (Value of n*(2*Value of n+1)*(2*Value of n-1))/3
  • sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4
  • sum_of_first_n_terms = (Value of n*(Value of n+1))/2
  • sum_of_first_n_terms = (Value of n*(Value of n+1)*(2*Value of n+1))/6
Where is the Sum of squares of first n even numbers calculator used?
Among many, Sum of squares of first n even numbers calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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