Sum of First N Terms of Harmonic Progression Calculator

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✖The Common Difference of HP is the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression.ⓘ Common Difference of HP [d]			+10% -10%
✖The First Term of HP is the value corresponding to the first term in the Harmonic Progression.ⓘ First term of HP [a]			+10% -10%
✖The Total Terms of HP is the total number of terms present in the given sequence of Harmonic Progression.ⓘ Total Terms of HP [n_Total]			+10% -10%

✖The Sum of First N Terms of HP is the summation of the terms starting from the first to the nth term of given Harmonic Progression.ⓘ Sum of First N Terms of Harmonic Progression [S_n]

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Formula

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Sum of First N Terms of Harmonic Progression

Formula

`"S"_{"n"} = (1/"d")*ln((2*"a"+(2*"n"_{"Total"}-1)*"d")/(2*"a"-"d"))`

Example

`"1.282475"=(1/"2")*ln((2*"3"+(2*"12"-1)*"2")/(2*"3"-"2"))`

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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 HP = (1/Common Difference of HP)*ln((2*First term of HP+(2*Total Terms of HP-1)*Common Difference of HP)/(2*First term of HP-Common Difference of HP))
S_n = (1/d)*ln((2*a+(2*n_Total-1)*d)/(2*a-d))
This formula uses 1 Functions, 4 Variables

Functions Used

ln - Natural logarithm function (base e), ln(Number)

Variables Used

Sum of First N Terms of HP - The Sum of First N Terms of HP is the summation of the terms starting from the first to the nth term of given Harmonic Progression.
Common Difference of HP - The Common Difference of HP is the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression.
First term of HP - The First Term of HP is the value corresponding to the first term in the Harmonic Progression.
Total Terms of HP - The Total Terms of HP is the total number of terms present in the given sequence of Harmonic Progression.

STEP 1: Convert Input(s) to Base Unit

Common Difference of HP: 2 --> No Conversion Required
First term of HP: 3 --> No Conversion Required
Total Terms of HP: 12 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n = (1/d)*ln((2*a+(2*n_Total-1)*d)/(2*a-d)) --> (1/2)*ln((2*3+(2*12-1)*2)/(2*3-2))

Evaluating ... ...

S_n = 1.28247467873077

STEP 3: Convert Result to Output's Unit

1.28247467873077 --> No Conversion Required

FINAL ANSWER

1.28247467873077 <-- Sum of First N Terms of HP

(Calculation completed in 00.000 seconds)

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Credits

Created by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has created this Calculator and 25+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< 2 Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression

Go Sum of First N Terms of HP = (1/Common Difference of HP)*ln((2*First term of HP+(2*Total Terms of HP-1)*Common Difference of HP)/(2*First term of HP-Common Difference of HP))

Nth Term of Harmonic Progression

Go Nth Term of HP = 1/(First term of HP+(Total Terms of HP-1)*Common Difference of HP)

Sum of First N Terms of Harmonic Progression Formula

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 HP = (1/Common Difference of HP)*ln((2*First term of HP+(2*Total Terms of HP-1)*Common Difference of HP)/(2*First term of HP-Common Difference of HP)) to calculate the Sum of First N Terms of HP, 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 HP 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 HP (d), First term of HP (a) & Total Terms of HP (n_Total) 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 -> 1.282475 = (1/2)*ln((2*3+(2*12-1)*2)/(2*3-2)).

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_Total-1)*d)/(2*a-d)) or Sum of First N Terms of HP = (1/Common Difference of HP)*ln((2*First term of HP+(2*Total Terms of HP-1)*Common Difference of HP)/(2*First term of HP-Common Difference of HP)). The Common Difference of HP is the difference of reciprocal of an arbitrary term from the reciprocal of its proceeding term of the Harmonic Progression, The First Term of HP is the value corresponding to the first term in the Harmonic Progression & The Total Terms of HP is the total number of terms present in the given sequence of Harmonic 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 HP = (1/Common Difference of HP)*ln((2*First term of HP+(2*Total Terms of HP-1)*Common Difference of HP)/(2*First term of HP-Common Difference of HP)). To calculate Sum of First N Terms of Harmonic Progression, you need Common Difference of HP (d), First term of HP (a) & Total Terms of HP (n_Total). With our tool, you need to enter the respective value for Common Difference of HP, First term of HP & Total Terms of HP 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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