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Sum of First N Terms of Harmonic Progression Formula

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The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression. Check FAQs

S n = (\frac{1}{d}) \cdot \ln (\frac{2 \cdot a + (2 \cdot n - 1) \cdot d}{2 \cdot a - d})

S_n - Sum of First N Terms of Progression?d - Common Difference of Progression?a - First Term of Progression?n - Index N of Progression?

Sum of First N Terms of Harmonic Progression Example

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Here is how the Sum of First N Terms of Harmonic Progression equation looks like with Values.

Here is how the Sum of First N Terms of Harmonic Progression equation looks like with Units.

Here is how the Sum of First N Terms of Harmonic Progression equation looks like.

0.8047 = (\frac{1}{4}) \cdot \ln (\frac{2 \cdot 3 + (2 \cdot 6 - 1) \cdot 4}{2 \cdot 3 - 4})

0.8047 = (\frac{1}{4}) \cdot \ln (\frac{2 \cdot 3 + (2 \cdot 6 - 1) \cdot 4}{2 \cdot 3 - 4})

0.8047 = (\frac{1}{4}) \cdot \ln (\frac{2 \cdot 3 + (2 \cdot 6 - 1) \cdot 4}{2 \cdot 3 - 4})

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Sum of First N Terms of Harmonic Progression Solution

Follow our step by step solution on how to calculate Sum of First N Terms of Harmonic Progression?

FIRST Step Consider the formula

S n = (\frac{1}{d}) \cdot \ln (\frac{2 \cdot a + (2 \cdot n - 1) \cdot d}{2 \cdot a - d})

Next Step Substitute values of Variables

∴

S n = (\frac{1}{4}) \cdot \ln (\frac{2 \cdot 3 + (2 \cdot 6 - 1) \cdot 4}{2 \cdot 3 - 4})

Next Step Prepare to Evaluate

∴

S n = (\frac{1}{4}) \cdot \ln (\frac{2 \cdot 3 + (2 \cdot 6 - 1) \cdot 4}{2 \cdot 3 - 4})

Next Step Evaluate

∴

S n = 0.80471895621705

LAST Step Rounding Answer

∴

S n = 0.8047

Sum of First N Terms of Harmonic Progression Formula Elements

Variables

Functions

Sum of First N Terms of Progression

The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression.

Symbol: S_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of First N Terms of Progression

Common Difference of Progression

The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

Symbol: d

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Common Difference of Progression

First Term of Progression

The First Term of Progression is the term at which the given Progression starts.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find First Term of Progression

Index N of Progression

The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Index N of Progression

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Harmonic Progression category

Go Common Difference of Harmonic Progression

d = (\frac{1}{T n} - \frac{1}{T n-1})

Go Nth Term of Harmonic Progression

T n = \frac{1}{a + (n - 1) \cdot d}

Go First Term of Harmonic Progression

a = \frac{1}{T n} - ((n - 1) \cdot d)

Go Nth Term of Harmonic Progression from End

T n = \frac{1}{l - (n - 1) \cdot d}

How to Evaluate Sum of First N Terms of Harmonic Progression?

Sum of First N Terms of Harmonic Progression evaluator uses Sum of First N Terms of Progression = (1/Common Difference of Progression)*ln((2*First Term of Progression+(2*Index N of Progression-1)*Common Difference of Progression)/(2*First Term of Progression-Common Difference of Progression)) to evaluate the Sum of First N Terms of Progression, The Sum of First N Terms of Harmonic Progression formula is defined as the summation of the terms starting from the first to the nth term of given Harmonic Progression. Sum of First N Terms of Progression is denoted by S_n symbol.

How to evaluate Sum of First N Terms of Harmonic Progression using this online evaluator? To use this online evaluator for Sum of First N Terms of Harmonic Progression, enter Common Difference of Progression (d), First Term of Progression (a) & Index N of Progression (n) and hit the calculate button.

FAQs on Sum of First N Terms of Harmonic Progression

What is the formula to find Sum of First N Terms of Harmonic Progression?

The formula of Sum of First N Terms of Harmonic Progression is expressed as Sum of First N Terms of Progression = (1/Common Difference of Progression)*ln((2*First Term of Progression+(2*Index N of Progression-1)*Common Difference of Progression)/(2*First Term of Progression-Common Difference of Progression)). Here is an example- 0.804719 = (1/4)*ln((2*3+(2*6-1)*4)/(2*3-4)).

How to calculate Sum of First N Terms of Harmonic Progression?

With Common Difference of Progression (d), First Term of Progression (a) & Index N of Progression (n) we can find Sum of First N Terms of Harmonic Progression using the formula - Sum of First N Terms of Progression = (1/Common Difference of Progression)*ln((2*First Term of Progression+(2*Index N of Progression-1)*Common Difference of Progression)/(2*First Term of Progression-Common Difference of Progression)). This formula also uses Natural Logarithm (ln) function(s).

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Sum of First N Terms of Harmonic Progression Formula

Sum of First N Terms of Harmonic Progression Example

Sum of First N Terms of Harmonic Progression Solution

Sum of First N Terms of Harmonic Progression Formula Elements

Other formulas in Harmonic Progression category

How to Evaluate Sum of First N Terms of Harmonic Progression?

FAQs on Sum of First N Terms of Harmonic Progression

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