geometric proofs math

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C(n,r) is the required combination by definition. Each of these combinations consists of a group of r dissimilar things, which can be arranged among themselves in P(r,r) = r! ways. But the number of permutations of n different things taken r at a time is P(n,r)..

From the definition of inverse of a matrix, we have (AB)(AB) - 1 = I or A - 1 (AB)(AB) - 1 = A - 1 I (Pre-multiplying both sides by A - 1 ) or (A - 1 A) B (AB) - 1 = A - 1 (Since A - 1 I = A - 1 ) or I B (AB) - 1 = A - 1 or B (AB) - 1 = A - 1 or (B - 1 B)(AB) - 1 =B - ..

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..

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 ..

i) The series formed by the reciprocals of the terms of a geometric series is also a geometric series. ii) There is no general method of finding the sum of a harmonic progressi..

1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, b-k, c-k are in A.P...