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))
Sn = (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
Sn = (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 ... ...
Sn = 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 00.020 seconds)

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
Mridul Sharma has verified this Calculator and 1700+ more calculators!

5 Harmonic Progression Calculators

Sum of First N Terms of Harmonic Progression
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
Go Index N of Progression = ((1/Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1
First Term of Harmonic Progression
Go First Term of Progression = 1/Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)
Nth Term of Harmonic Progression
Go Nth Term of Progression = 1/(First Term of Progression+(Index N of Progression-1)*Common Difference of Progression)
Common Difference of Harmonic Progression
Go Common Difference of Progression = (1/Nth Term of Progression-1/(N-1)th Term of Progression)

4 Harmonic Progression Calculators

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

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))
Sn = (1/d)*ln((2*a+(2*n-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 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 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 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 Sn = (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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!