Here you will learn some sequences and series examples for better understanding of sequences and series concepts. Example 1 : If ∑nr=1Tr = n8 (n + 1)(n + 2)(n + 3), then find ∑nr=11Tr Solution : ∵ Tn = Sn–Sn−1 = ∑nr=1Tr – \({\sum}_{r=1}^{n […]
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Here you will learn method of difference in sequences and series with examples. Let’s begin – Method of Difference Some times the nth 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
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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)
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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
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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. an+1 – an = constant (=d) for all n ∈ N The constant
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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 + 5x2
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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
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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 a1 + a2 + a3 + ……… + an is an HP
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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
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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 a1, a2, a3,………,an the corresponding series is a1 + a2 + a3 + ……… + an
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