Sum of Cubes of First N Even Numbers Calculator

✖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 Cubes of First N Even Natural Numbers is the summation of cubes of the even natural numbers starting from 1 to the nth even number 2n.ⓘ Sum of Cubes of First N Even Numbers [S_n3(Even)]

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Formula

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Sum of Cubes of First N Even Numbers

Formula

`"S"_{"n3(Even)"} = 2*("n"*("n"+1))^2`

Example

`"288"=2*("3"*("3"+1))^2`

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Sum of Cubes of First N Even Numbers Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Cubes of First N Even Natural Numbers = 2*(Value of N*(Value of N+1))^2
S_n3(Even) = 2*(n*(n+1))^2
This formula uses 2 Variables

Variables Used

Sum of Cubes of First N Even Natural Numbers - The Sum of Cubes of First N Even Natural Numbers is the summation of cubes of the even natural numbers starting from 1 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_n3(Even) = 2*(n*(n+1))^2 --> 2*(3*(3+1))^2

Evaluating ... ...

S_n3(Even) = 288

STEP 3: Convert Result to Output's Unit

288 --> No Conversion Required

FINAL ANSWER

288 <-- Sum of Cubes of First N Even Natural Numbers

(Calculation completed in 00.004 seconds)

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Credits

Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 200+ more calculators!

Verified by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 3 Sum of Cubes Calculators

Sum of Cubes of First N Odd Numbers

Go Sum of Cubes of First N Odd Natural Numbers = (Value of N)^2*(2*(Value of N)^2-1)

Sum of Cubes of First N Even Numbers

Go Sum of Cubes of First N Even Natural Numbers = 2*(Value of N*(Value of N+1))^2

Sum of Cubes of First N Natural Numbers

Go Sum of Cubes of First N Natural Numbers = ((Value of N*(Value of N+1))^2)/4

Sum of Cubes of First N Even Numbers Formula

Sum of Cubes of First N Even Natural Numbers = 2*(Value of N*(Value of N+1))^2
S_n3(Even) = 2*(n*(n+1))^2

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 Cubes of First N Even Numbers?

Sum of Cubes of First N Even Numbers calculator uses Sum of Cubes of First N Even Natural Numbers = 2*(Value of N*(Value of N+1))^2 to calculate the Sum of Cubes of First N Even Natural Numbers, Sum of Cubes of First N Even Numbers formula is defined as the summation of cubes of the even natural numbers starting from 1 to the nth even number 2n. Sum of Cubes of First N Even Natural Numbers is denoted by S_n3(Even) symbol.

How to calculate Sum of Cubes of First N Even Numbers using this online calculator? To use this online calculator for Sum of Cubes of First N Even Numbers, enter Value of N (n) and hit the calculate button. Here is how the Sum of Cubes of First N Even Numbers calculation can be explained with given input values -> 288 = 2*(3*(3+1))^2.

FAQ

What is Sum of Cubes of First N Even Numbers?

Sum of Cubes of First N Even Numbers formula is defined as the summation of cubes of the even natural numbers starting from 1 to the nth even number 2n and is represented as S_n3(Even) = 2*(n*(n+1))^2 or Sum of Cubes of First N Even Natural Numbers = 2*(Value of N*(Value of N+1))^2. 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 Cubes of First N Even Numbers?

Sum of Cubes of First N Even Numbers formula is defined as the summation of cubes of the even natural numbers starting from 1 to the nth even number 2n is calculated using Sum of Cubes of First N Even Natural Numbers = 2*(Value of N*(Value of N+1))^2. To calculate Sum of Cubes 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.

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