The harmonic series is one of the three primary series of algebra, the arithmetic series and geometric series being the other two. This is one of the fundamental concepts of mathematic algebra and is considered a reciprocal of the arithmetic series. Being a part of advanced mathematics, harmonic series is taught extensively at undergraduate, post-graduate, and other higher levels.
Harmonic series and harmonic sequences are highly intertwined and come hand in hand. Students of algebra are given numerous academic writing works to prove their mathematical knowledge and compatibilities. But sometimes they find themselves trapped in these assignments due to various reasons. If you are also facing any problems in writing a proper harmonic series assignment, contact EssayCorp to get the best mathematics assignment help at the most affordable price.
What is Harmonic Series?
To understand the harmonic series, we must first understand the harmonic sequence, for harmonic series is the total of harmonic sequences. A harmonic sequence is a sequence of fractional terms wherein the difference between denominators of two successive is the same.
For example, 12, 13, 14, 15... is a harmonic sequence.
To get the harmonic series we just need to add all the terms of the sequence. Which will give the equation- 12+13+14+15+... This is the harmonic series.
If you observe carefully, you will find that a harmonic sequence is nothing but a sequence that has reciprocals of an arithmetic sequence’s terms. But be careful, this similarity does not mean that the sum of this sequence, i.e., harmonic series, is the reciprocal of the sum of an arithmetic sequence.
Difference Between HS, AS, and GS
As we have observed above, HS is a series that contains the reciprocal of the terms of AS. But their functioning and mathematical operations are way different from each other. Similarly, the 3rd fundamental series, i.e., Geometric Sequence (GS), has its own properties and functions. Let us discuss the basics of these series one by one.
Arithmetic Sequence: An arithmetic sequence is a series where the difference between two consecutive terms is always constant. For example, 1,2,3,4,5….. Is an arithmetic sequence.
The equation for an AP is as follows: a, a+d, a+2d, a+3d,...
The sequence formula for the nth term of AS is: an=a+ (n-1)d
And its sum is: Sn=n2(2a+(n-1)d)
Harmonic Sequence: As we know, an HS is a series wherein the terms of an AS are in reciprocal form. Here, the difference between denominators of the two consecutive terms is always constant.
The equation of an HS is as follows: 1a, 1a+d, 1a+2d,...
The sequence formula of the nth term of an HS is: an=1a+(n-1)d
And the sum of an HS is: Sn=1dln(2a+(2n-1)d2a-d
Geometric Sequence: Geometric sequence is the sequence wherein by dividing a number from the one which is just before it is always the same. Thus, a GS has a common divisor for any two consecutive terms.
The equation of a GS is: a, ar1, ar2, ar3.... where “a” is the first term and “r” is the common ratio, aka common divisor.
The sequence formula to determine the nth term of a GS is: an=ar(n-1)
The sum formula for a GS of ‘n’ terms is: Sn=a(1-rn)1-r
The series formula for the sum of infinite terms: Sn=a1-r where r<1
Harmonic Sequence Assignments
Assignment work is something that universities assign to their students to check and evaluate the knowledge and capabilities of their students objectively. These assignments are also utilized to bring out the areas of further development and finally to craft results. Such academic works also help students gain various skills and many practical knowledge.
A student learns to conduct research and extract relevant information from various sources like books, journals, and the internet. Besides that, students also learn about the utilization of algebraic fundamentals in real-life situations like the mixing of ingredients in proper proportions to cook a recipe.
Also, algebraic assignments help students in learning the ways and methods for analyzing the gathered data and representing it properly and aesthetically. Thus, academic writing tasks help learners to develop their mindset in a critical and logical manner.
Problems With Algebraic Assignments
While working on their writing projects of algebra, students often face numerous difficulties like time management, lack of relevant knowledge, absence of required resources, and various other problems. The following points can be read to understand the issues associated with harmonic series assignments:
Computational Weaknesses: Even if they have a good understanding of mathematical concepts, students often misread the numbers and operations that create computational problems. This impacts the quality of the project.
Incomplete Knowledge: Being a highly complex subject, mathematical assignments require in-depth knowledge of all the relevant concepts and fundamentals. But not all students are well-acquainted with the necessary knowledge which reduces the quality of their projects.
Difficulty in Connections: Many times, students find it difficult to properly make connections across different mathematical expressions and equations. For example, they may find it difficult in understanding the relation between the alphabet and the values assigned to them.
The problem in Connecting Maths with Reality: Primarily, mathematics is abstract. Therefore, students find it difficult to connect its concepts with the real world. This inability reduces the authenticity and relevance of the project for students in real-life scenarios.
Time Issues: While working on their algebra assignments, students face difficulty in gathering the relevant knowledge and representing it adequately in a time-bound manner. Due to these issues, they are not able to submit the assignment timely and, thus, they failed the project.
Algebraic Assignment Help
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The harmonic sequence is a critical aspect of algebra. At the same time, it's quite difficult to handle its term papers, projects, assessments, etc. efficiently. If you are also facing some problems in completing your mathematical assignments, contact EssayCorp now and grab the opportunity to earn an A+ in your maths assignments.