## 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))
Sn = (1/d)*ln((2*a+(2*nTotal-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
Sn = (1/d)*ln((2*a+(2*nTotal-1)*d)/(2*a-d)) --> (1/2)*ln((2*3+(2*12-1)*2)/(2*3-2))
Evaluating ... ...
Sn = 1.28247467873077
STEP 3: Convert Result to Output's Unit
1.28247467873077 --> No Conversion Required
1.28247467873077 <-- Sum of First N Terms of HP
(Calculation completed in 00.000 seconds)
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Indian Institute of Information Technology (IIIT), Guwahati
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## < 2 Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression
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
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

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))
Sn = (1/d)*ln((2*a+(2*nTotal-1)*d)/(2*a-d))

## 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 Sn 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 (nTotal) 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 Sn = (1/d)*ln((2*a+(2*nTotal-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 (nTotal). 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. Let Others Know