Sequences and Series Examples
>These formulae are used when 'last term' is given. (v) If 'a' and 'r' be the first term and common ratio of a G.P. such (vi) If the sequence a, G 1 , G 2 ,....,G n , b of positive numbers is a G.P., then the numbers G 1 , G 2 ,....,G n , are called the n geometric means between a and b. (vii) The ..
>These formulae are used when 'last term' is given. (v) If 'a' and 'r' be the first term and common ratio of a G.P. such (vi) If the sequence a, G 1 , G 2 ,....,G n , b of positive numbers is a G.P., then the numbers G 1 , G 2 ,....,G n , are called the n geometric means between a and b. (vii) The ..Series
Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...
Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...Sequences and Series
A set of numbers arranged in a definite order according to some definite rule is called a sequence. A sequence is a function whose domain is the set N of natural numbers. Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the..
General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..Sequences and Series
Sequence - A set of numbers arranged in a definite order according to some definite rule is called a sequence. or A sequence is a function whose domain is the set N of natural numbers. It is customary to denote a sequence by a letter 'a' and the image a(n) or t(n), n N under 'a' by a n or t ..
Arithmetic Geometric Series
A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..
A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..Examples:
i) 1 + 4 + 7 + 10 + ... is a series in which first term is 1, second term is 4, third term is 7 and so on. ii) 3 - 9 + 27 - 81 + ... is also a series in which the first term is 3, second term is -9, third term is 27 and so ..
Geometric Progressions (G.P.)
The series of terms a, ar, ar 2 , ar 3 ,.... in which each term bears a constant ratio to the preceeding term is a geometric progression. The constant ratio is called the common rati..
Geometric Progressions (G.P.)
The series of terms a, ar, ar 2 , ar 3 ,.... in which each term bears a constant ratio to the preceeding term is a geometric progression. The constant ratio is called the common ratio.OR A geometrical progression is a succession of terms such that each term bears fixed ratio to the precee..
Geometric Progressions (G.P.)
Geometric Progressions (G.P.) - The series of terms a, ar, ar 2 , ar 3 ,.... in which each term bears a constant ratio to the preceeding term is a geometric progression. The constant ratio is called the common ratio.OR A geometrical progression is a succession of terms such that each term..
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