Sum of squares of first n natural numbers Calculator

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

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✖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 squares of first n natural numbers [S_n]

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Sum of squares of first n natural numbers

Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 100+ more calculators!

Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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

< 11 Other formulas that you can solve using the same Inputs

Sum of last n terms in a finite AP with first term, total terms given

Sum of last n terms=(value of n*(2*First term+Common difference*(2*total terms-value of n-1)))/2 GO

Sum of squares of first n even numbers

Sum of squares of first n even numbers=(2*value of n*(value of n+1)*(2*value of n+1))/3 GO

Sum of Squares first n odd numbers

Sum of squares first n odd numbers=(value of n*(2*value of n+1)*(2*value of n-1))/3 GO

Sum of last n terms in a finite AP with last term given

Sum of last n terms=((value of n*(2*Last term+Common difference*(1-value of n)))/2) GO

Sum of first n terms in a finite GP

Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1) GO

nth term from end in a finite GP

Nth term=First term*(Common Ratio^(total terms-value of n)) 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

Nth term of GP

Nth term=First term*(Common Ratio^(value of n-1)) GO

nth term from the end of finite GP when last term and common ratio is given

Nth term=Last term/(Common Ratio^(value of n-1)) GO

Sum of first n even natural numbers

Sum of First n terms=(value of n*(value of n+1)) GO

< 10 Other formulas that calculate the same Output

Sum of first n terms of AGP

Sum of First n terms=((First term-(First term+(total terms-1)*Common difference)*(Common Ratio^total terms))/(1-Common Ratio))+(Common difference*Common Ratio*(1-Common Ratio^(total terms-1))/(1-Common Ratio)^2) GO

Sum of first n terms in an AP when common difference is given

Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference) GO

Sum of first n terms where r>1

Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1)) GO

Sum of first n terms in a finite GP

Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1) GO

Sum of first n terms in an AP when last term is given

Sum of First n terms=(total terms/2)*(First term+Last term) 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 infinite GP when r is less than one

Sum of First n terms=First term/(1-Common Ratio) GO

Sum of first n even natural numbers

Sum of First n terms=(value of n*(value of n+1)) GO

Sum of first n odd natural numbers

Sum of First n terms=(value of n)^2 GO

Sum of squares of first n natural numbers Formula

Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6
S<sub>n</sub>=(n*(n+1)*(2*n+1))/6

More formulas

Sum of first n natural numbers GO

Sum of cubes of first n natural numbers GO

Sum of Squares first n odd numbers GO

Sum of squares of first n even numbers GO

Sum of first n even natural numbers GO

Sum of first n odd natural numbers GO

Sum of cubes of first n even numbers GO

Sum of n natural numbers taken power of 4(four) GO

What does the squares of natural numbers mean?

Squares of natural numbers simply means squaring the natural numbers. Example - squares of natural numbers are 1,4,9,16,25,36 and so on.

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

Sum of squares of first n natural numbers calculator uses Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6 to calculate the Sum of First n terms, Sum of squares of first n natural numbers can be calculated by using the formula( n(n+1)(2*n+1))/6 . Sum of squares of first 4 natural numbers (1,4,9,16) is 30. Sum of First n terms and is denoted by S_n symbol.

How to calculate Sum of squares of first n natural numbers using this online calculator? To use this online calculator for Sum of squares of first n natural numbers, enter value of n (n) and hit the calculate button. Here is how the Sum of squares of first n natural numbers calculation can be explained with given input values -> 1 = (1*(1+1)*(2*1+1))/6.

FAQ

What is Sum of squares of first n natural numbers?

Sum of squares of first n natural numbers can be calculated by using the formula( n(n+1)(2*n+1))/6 . Sum of squares of first 4 natural numbers (1,4,9,16) is 30 and is represented as S_n=(n*(n+1)*(2*n+1))/6 or Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6. 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 natural numbers?

Sum of squares of first n natural numbers can be calculated by using the formula( n(n+1)(2*n+1))/6 . Sum of squares of first 4 natural numbers (1,4,9,16) is 30 is calculated using Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6. To calculate Sum of squares 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 10 other way(s) to calculate the same, which is/are as follows -

Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference)
Sum of First n terms=(total terms/2)*(First term+Last term)
Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1)
Sum of First n terms=First term/(1-Common Ratio)
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)/4
Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1))
Sum of First n terms=((First term-(First term+(total terms-1)*Common difference)*(Common Ratio^total terms))/(1-Common Ratio))+(Common difference*Common Ratio*(1-Common Ratio^(total terms-1))/(1-Common Ratio)^2)
Sum of First n terms=(value of n*(value of n+1))
Sum of First n terms=(value of n)^2

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