Sum of Squares of First N Even Natural Numbers Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3
Sn2(Even) = (2*n*(n+1)*((2*n)+1))/3
This formula uses 2 Variables
Variables Used
Sum of Squares of First N Even Natural Numbers - The Sum of Squares of First N Even Natural Numbers is the summation of squares of the even natural numbers starting from 2 to the nth even number 2n.
Value of N - The Value of N is the total number of terms from the beginning of the series up to where the sum of series is calculating.
STEP 1: Convert Input(s) to Base Unit
Value of N: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Sn2(Even) = (2*n*(n+1)*((2*n)+1))/3 --> (2*3*(3+1)*((2*3)+1))/3
Evaluating ... ...
Sn2(Even) = 56
STEP 3: Convert Result to Output's Unit
56 --> No Conversion Required
FINAL ANSWER
56 <-- Sum of Squares of First N Even Natural Numbers
(Calculation completed in 00.004 seconds)

Credits

Created by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
Dipto Mandal has created this Calculator and 25+ more calculators!
Verified by Alithea Fernandes
Don Bosco College of Engineering (DBCE), Goa
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3 Sum of Squares Calculators

Sum of Squares of First N Odd Natural Numbers
Go Sum of Squares of First N Odd Natural Numbers = (Value of N*((2*Value of N)+1)*((2*Value of N)-1))/3
Sum of Squares of First N Even Natural Numbers
Go Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3
Sum of Squares of First N Natural Numbers
Go Sum of Squares of First N Natural Numbers = (Value of N*(Value of N+1)*((2*Value of N)+1))/6

Sum of Squares of First N Even Natural Numbers Formula

Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3
Sn2(Even) = (2*n*(n+1)*((2*n)+1))/3

What is a General Series?

Suppose a1, a2, a3, …, an is a sequence such that the expression a1 + a2 + a3 +,…+ an is called the series associated with the given sequence.

Where are Series used?

Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance.

How to Calculate Sum of Squares of First N Even Natural Numbers?

Sum of Squares of First N Even Natural Numbers calculator uses Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3 to calculate the Sum of Squares of First N Even Natural Numbers, The Sum of Squares of First N Even Natural Numbers formula is defined as the summation of squares of the even natural numbers starting from 2 to the nth even number 2n. Sum of Squares of First N Even Natural Numbers is denoted by Sn2(Even) symbol.

How to calculate Sum of Squares of First N Even Natural Numbers using this online calculator? To use this online calculator for Sum of Squares of First N Even Natural Numbers, enter Value of N (n) and hit the calculate button. Here is how the Sum of Squares of First N Even Natural 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 Natural Numbers?
The Sum of Squares of First N Even Natural Numbers formula is defined as the summation of squares of the even natural numbers starting from 2 to the nth even number 2n and is represented as Sn2(Even) = (2*n*(n+1)*((2*n)+1))/3 or Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3. The Value of N is the total number of terms from the beginning of the series up to where the sum of series is calculating.
How to calculate Sum of Squares of First N Even Natural Numbers?
The Sum of Squares of First N Even Natural Numbers formula is defined as the summation of squares of the even natural numbers starting from 2 to the nth even number 2n is calculated using Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3. To calculate Sum of Squares of First N Even Natural 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.
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