Sum of cubes of first n natural numbers Calculator

Main Category	Math ↺
Math	Sequence and Series ↺
Sequence and Series	General Series ↺

✖Value of n is the index value of position n in a series or a sequence.ⓘ Value of n [n]

+10%

-10%

✖Sum of First n terms denoted the sum of first n terms occuring in a progression like Arithematic Progression, Geometric Progression, Harmonic Progression.ⓘ Sum of cubes of first n natural numbers [S_n]

⎘ Copy

👎

Formula

Reset

👍

Credits

Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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

Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1000+ more calculators!

Sum of cubes of first n natural numbers Solution

STEP 0: Pre-Calculation Summary

Formula Used

sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4
S_n = ((n*(n+1))^2)/4
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

S_n = ((n*(n+1))^2)/4 --> ((3*(3+1))^2)/4

Evaluating ... ...

S_n = 36

STEP 3: Convert Result to Output's Unit

36 --> No Conversion Required

FINAL ANSWER

36 <-- Sum of First n terms

(Calculation completed in 00.000 seconds)

You are here

< 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 cubes of first n natural numbers Formula

sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4
S_n = ((n*(n+1))^2)/4

What does cubes of first n natural numbers mean?

Cubes of first n natural numbers simply means natural numbers raised to a power of 3. e.g- some of the cubes of starting natural numbers are 1,8,27,64,125 & so on.

How to Calculate Sum of cubes of first n natural numbers?

Sum of cubes of first n natural numbers calculator uses sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4 to calculate the Sum of First n terms, Sum of cubes of first n natural numbers can be calculated using the formula [n*(n+1)/2]^2. Sum of cubes of first 4 natural numbers (1 ->1, 2 ->8, 3 ->27, 4->64) is 100. Sum of First n terms and is denoted by S_n symbol.

How to calculate Sum of cubes of first n natural numbers using this online calculator? To use this online calculator for Sum of cubes of first n natural numbers, enter Value of n (n) and hit the calculate button. Here is how the Sum of cubes of first n natural numbers calculation can be explained with given input values -> 36 = ((3*(3+1))^2)/4.

FAQ

What is Sum of cubes of first n natural numbers?

Sum of cubes of first n natural numbers can be calculated using the formula [n*(n+1)/2]^2. Sum of cubes of first 4 natural numbers (1 ->1, 2 ->8, 3 ->27, 4->64) is 100 and is represented as S_n = ((n*(n+1))^2)/4 or sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4. Value of n is the index value of position n in a series or a sequence.

How to calculate Sum of cubes of first n natural numbers?

Sum of cubes of first n natural numbers can be calculated using the formula [n*(n+1)/2]^2. Sum of cubes of first 4 natural numbers (1 ->1, 2 ->8, 3 ->27, 4->64) is 100 is calculated using sum_of_first_n_terms = ((Value of n*(Value of n+1))^2)/4. To calculate Sum of cubes of first n 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.

How many ways are there to calculate Sum of First n terms?

In this formula, Sum of First n terms 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

Facebook
Twitter
WhatsApp
Reddit
LinkedIn
E-Mail

Let Others Know

✖

Facebook

Twitter

Copied!