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Sum of First N Terms of Harmonic Progression Calculator

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✖The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.ⓘ Common Difference of Progression [d]			+10% -10%
✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.ⓘ Index N of Progression [n]			+10% -10%

✖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.ⓘ Sum of First N Terms of Harmonic Progression [S_n]

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Sum of First N Terms of Harmonic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
S_n = (1/d)*ln((2*a+(2*n-1)*d)/(2*a-d))
This formula uses 1 Functions, 4 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

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.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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.

STEP 1: Convert Input(s) to Base Unit

Common Difference of Progression: 4 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n = (1/d)*ln((2*a+(2*n-1)*d)/(2*a-d)) --> (1/4)*ln((2*3+(2*6-1)*4)/(2*3-4))

Evaluating ... ...

S_n = 0.80471895621705

STEP 3: Convert Result to Output's Unit

0.80471895621705 --> No Conversion Required

FINAL ANSWER

0.80471895621705 ≈ 0.804719 <-- Sum of First N Terms of Progression

(Calculation completed in 00.004 seconds)

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Indian Institute of Information Technology (IIIT), Guwahati

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< Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

LaTeX Go 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))

Number of Terms of Harmonic Progression

LaTeX Go Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1

Nth Term of Harmonic Progression

LaTeX Go Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of Progression)

Common Difference of Harmonic Progression

LaTeX Go Common Difference of Progression = (1/Nth Term of Progression-1/(N-1)th Term of Progression)

< Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

First Term of Harmonic Progression

LaTeX Go First Term of Progression = 1/Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)

Nth Term of Harmonic Progression

LaTeX Go Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of Progression)

Common Difference of Harmonic Progression

LaTeX Go Common Difference of Progression = (1/Nth Term of Progression-1/(N-1)th Term of Progression)

Sum of First N Terms of Harmonic Progression Formula

LaTeX Go

What is a Harmonic Progression?

In Mathematics, a Harmonic Progression is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence is a Harmonic Progression when each term is the harmonic mean of the neighboring terms.

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

Sum of First N Terms of Harmonic Progression calculator 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 calculate 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 calculate Sum of First N Terms of Harmonic Progression using this online calculator? To use this online calculator 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. Here is how the Sum of First N Terms of Harmonic Progression calculation can be explained with given input values -> 0.804719 = (1/4)*ln((2*3+(2*6-1)*4)/(2*3-4)).

FAQ

What is Sum of First N Terms of Harmonic 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 and is represented as S_n = (1/d)*ln((2*a+(2*n-1)*d)/(2*a-d)) or 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)). The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant, The First Term of Progression is the term at which the given Progression starts & The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

How to calculate Sum of First N Terms of Harmonic 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 is calculated using 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 calculate Sum of First N Terms of Harmonic Progression, you need Common Difference of Progression (d), First Term of Progression (a) & Index N of Progression (n). With our tool, you need to enter the respective value for Common Difference of Progression, First Term of Progression & Index N of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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