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Sum of Squares of First N Even Natural Numbers Calculator

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✖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.ⓘ Value of N [n]

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✖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.ⓘ Sum of Squares of First N Even Natural Numbers [S_n2(Even)]

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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
S_n2(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

S_n2(Even) = (2*n*(n+1)*((2*n)+1))/3 --> (2*3*(3+1)*((2*3)+1))/3

Evaluating ... ...

S_n2(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)

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Created by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

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Verified by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

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< Sum of Squares Calculators

Sum of Squares of First N Odd Natural Numbers

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX Go

Sum of Squares of First N Even Natural Numbers = (2*Value of N*(Value of N+1)*((2*Value of N)+1))/3
S_n2(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 S_n2(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 S_n2(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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