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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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Home » Math » Sequence and Series » AP,GP and HP » Sum of First N Terms of Harmonic Progression

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.

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.

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.

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.

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

Syntax: ln(Number)

Credits

Created by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has created this Formula and 25+ more formulas!

Verified by

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Formula and 1700+ more formulas!

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

Credits

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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