Here you will learn some sequences and series examples for better understanding of sequences and series concepts. Example 1 : If \({\sum}_{r=1}^{n} T_r\) = \(n\over 8\) (n + 1)(n + 2)(n + 3), then find \({\sum}_{r=1}^{n} \)\(1\over T_r\) Solution : \(\because\) \(T_n\) = \(S_n – S_{n-1}\) = \({\sum}_{r=1}^{n} T_r\) – \({\sum}_{r=1}^{n …
Here you will learn method of difference in sequences and series with examples. Let’s begin – Method of Difference Some times the \(n^{th}\) term of a sequence or a series can not be determined by the method, we have discussed earlier. So we compute the difference between the successive terms of given sequence for obtained …
Here you will learn sum of gp to infinity (sum of infinite gp) and its proof with examples. Let’s begin – Sum of GP to Infinity (Sum of Infinite GP) The sum of an infinite GP with first term a and common ratio r(-1 < r < 1 i.e. , | r | < 1) …
Here you will learn what is geometric progression and formula for geometric progression with examples. Let’s begin – Geometric Progression (GP) A sequence of non-zero numbers is called a geometric progression (GP) if the ratio of a term and the term preceding to its always a constant quantity. The constant ratio is called the common …
Here you you will learn what is arithmetic progression (AP) and formula for arithmetic progression. Let’s begin – Arithmetic Progression (AP) A sequence is called an arithmetic progression if the difference of a term and the previous term is always same i.e. \(a_{n+1}\) – \(a_n\) = constant (=d) for all n \(\in\) N The constant …
Here you will learn what is agp (Arithmetico Geometric Series) and how to solve agp series. Let’s begin – What is AGP (Arithmetico – Geometric series) A series, each term of which is formed by multiplying the corresponding term of an A.P. & G.P. is called the Arithmetico-Geometric Series, e.g. 1 + 3x + 5\(x^2\) …
Here you will learn formula for arithmetic geometric and harmonic mean and relation between arithmetic geometric and harmonic mean. Let’s begin – Arithmetic Mean Formula If three terms are in A.P. then the middle term is called the A.M. between the other two, so if a, b, c are in A.P., b is A.M. of …
Relation Between Arithmetic Geometric and Harmonic mean Read More »
Here you will learn what is harmonic progression (hp) and sum of harmonic progression (hp series). Let’s begin – Sum of Harmonic Progression A sequence is said to be in H.P. if the reciprocal of its terms are in A.P. If the sequence \(a_1\) + \(a_2\) + \(a_3\) + ……… + \(a_n\) is an HP …
Here you will learn what is geometric progression (gp) and sum of gp series formula and properties of gp. Let’s begin – Sum of GP Series Formula G.P. is a sequence of non zero numbers each of the succeeding term is equal to the preceding term multiplied by a constant. Thus in GP the ratio …
Here, you will learn what is arithmetic progression (ap) and formula for sum of ap series and properties of ap. Let’s begin – The indicated sum of the terms of a sequence. In the case of a finite sequence \(a_1\), \(a_2\), \(a_3\),………,\(a_n\) the corresponding series is \(a_1\) + \(a_2\) + \(a_3\) + ……… + \(a_n\) …
