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Sum of Squares of First N Natural Numbers Formula

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The Sum of Squares of First N Natural Numbers is the summation of squares of the natural numbers starting from 1 to the nth natural number. Check FAQs

S n2 = \frac{n \cdot (n + 1) \cdot ((2 \cdot n) + 1)}{6}

S_n2 - Sum of Squares of First N Natural Numbers?n - Value of N?

Sum of Squares of First N Natural Numbers Example

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Here is how the Sum of Squares of First N Natural Numbers equation looks like with Values.

Here is how the Sum of Squares of First N Natural Numbers equation looks like with Units.

Here is how the Sum of Squares of First N Natural Numbers equation looks like.

14 = \frac{3 \cdot (3 + 1) \cdot ((2 \cdot 3) + 1)}{6}

14 = \frac{3 \cdot (3 + 1) \cdot ((2 \cdot 3) + 1)}{6}

14 = \frac{3 \cdot (3 + 1) \cdot ((2 \cdot 3) + 1)}{6}

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Sum of Squares of First N Natural Numbers Solution

Follow our step by step solution on how to calculate Sum of Squares of First N Natural Numbers?

FIRST Step Consider the formula

S n2 = \frac{n \cdot (n + 1) \cdot ((2 \cdot n) + 1)}{6}

Next Step Substitute values of Variables

∴

S n2 = \frac{3 \cdot (3 + 1) \cdot ((2 \cdot 3) + 1)}{6}

Next Step Prepare to Evaluate

∴

S n2 = \frac{3 \cdot (3 + 1) \cdot ((2 \cdot 3) + 1)}{6}

LAST Step Evaluate

∴

S n2 = 14

Sum of Squares of First N Natural Numbers Formula Elements

Variables

Sum of Squares of First N Natural Numbers

The Sum of Squares of First N Natural Numbers is the summation of squares of the natural numbers starting from 1 to the nth natural number.

Symbol: S_n2

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sum of Squares of First N Natural Numbers

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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of N

Other formulas in Sum of Squares category

Go Sum of Squares of First N Odd Natural Numbers

S n2(Odd) = \frac{n \cdot ((2 \cdot n) + 1) \cdot ((2 \cdot n) - 1)}{3}

Go Sum of Squares of First N Even Natural Numbers

S n2(Even) = \frac{2 \cdot n \cdot (n + 1) \cdot ((2 \cdot n) + 1)}{3}

How to Evaluate Sum of Squares of First N Natural Numbers?

Sum of Squares of First N Natural Numbers evaluator uses Sum of Squares of First N Natural Numbers = (Value of N*(Value of N+1)*((2*Value of N)+1))/6 to evaluate the Sum of Squares of First N Natural Numbers, The Sum of Squares of First N Natural Numbers formula is defined as the summation of squares of the natural numbers starting from 1 to the nth natural number. Sum of Squares of First N Natural Numbers is denoted by S_n2 symbol.

How to evaluate Sum of Squares of First N Natural Numbers using this online evaluator? To use this online evaluator for Sum of Squares of First N Natural Numbers, enter Value of N (n) and hit the calculate button.

FAQs on Sum of Squares of First N Natural Numbers

What is the formula to find Sum of Squares of First N Natural Numbers?

The formula of Sum of Squares of First N Natural Numbers is expressed as Sum of Squares of First N Natural Numbers = (Value of N*(Value of N+1)*((2*Value of N)+1))/6. Here is an example- 14 = (3*(3+1)*((2*3)+1))/6.

How to calculate Sum of Squares of First N Natural Numbers?

With Value of N (n) we can find Sum of Squares of First N Natural Numbers using the formula - Sum of Squares of First N Natural Numbers = (Value of N*(Value of N+1)*((2*Value of N)+1))/6.

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