grade 1 math!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

General Series - 1. To find the sum of first n natural numbers. ..

Permutations and Combinations..

A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n. In this square matrix of order n the elements a 1 1 , a 2 2 .......a n n is called the principal diagonal or the leading diagonal. The elements a 1 ..

If two events E 1 and E 2 can occur independently in exactly m ways and n ways respectively, then either of the two events can occur in (m + n) way..

2, 5, 8, 11, 14 , 32 37, 33 , 1 A sequence is called infinite if the number of terms is infinite. An infinite sequence has no last term. In this sequence, every term is followed by a new ter..

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..

i) Here, the total number = 6 + 6 = 12. 12 persons can be arranged in circular permutation as (12 - 1)! = 11! ways. ii) When 6 gentlemen are arranged around a table, there are 6 positions, each being between two gentlemen for 6 ladies, when no two ladies sit side by side. Now, the number..

Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 Since area has to be a positive quantity, it is gi..

Each circular permutation corresponds to n linear permutations depending on where we start. Since there are exactly n! linear permutations, there are exactly permutations. Hence, the number of circular permutations is the same as (n-1)..

Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and ..