middle school math course 1

\ n = ..

If we put r = n in the above formula, the..

Consider the GP a, ar, ar 2 ... ..

A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..

The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any ..

Harmonic Mean (H.M.) - If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other two. Example: 1/3, 1/7, 1/11 are in H.P., then 1/7 is the middle term. Hence 1/7 is th..

We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..

1. O!= 1 2. When n is a negative or fraction, n! is not defined...

Circular Permutations - When things are arranged in places along a line with first and last place, they form a linear permutation. So far we have dealt only with linear permutations. When things are arranged in places along a closed curve or a circle, in which any place may be regarded as the first..

P(n,r) is the number of permutations of n dissimilar things taken r at a time. These permutations can be divided into two groups. (i) Those not containing a particular thing l . (ii) Those containing a particular thing l . Taking out l from the given things, we have (n-1) things wh..