Proof:
..
..Note:
1. O!= 1 2. When n is a negative or fraction, n! is not defined...
1. O!= 1 2. When n is a negative or fraction, n! is not defined...Theorem:
The number of permutations of n dissimilar things taken r ..
The number of permutations of n dissimilar things taken r ..Corollary 3:
..
..Arithmetic Mean (A.M.)
1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted between a and b so that ..
1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted between a and b so that ..General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..Suggested answer:
. . . . . . . . . . . . Adding vertically, ..
. . . . . . . . . . . . Adding vertically, ..Examples:
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..To find the sum to infinity of a GP when the common ratio r is numerically less than 1
Consider the GP a, ar, ar 2 ... ..
Consider the GP a, ar, ar 2 ... ..Harmonic Progression (H.P.)
A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..
A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..See what our Users say :
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