two number cubes

where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural numbers. 4. Method of finding sum of a series whose nth term is know..

Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 ..

If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all appr..

of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficients in the..

The ratio obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio. is sub-triplicate ratio of a : b. For example the sub-triplicate ratio of 8a 3 : 27b 6 is or 2a : 3b 2 . Find the compounded ratio of the duplicate ratio of ..

When two number cubes are rolled, what is the probability of getting 11 as the product of the two numbers? => 0 or 1 11 or 1 9 or 5 36..

When two number cubes are rolled, what is the probability of getting 19 as the product of the two numbers? => 1 19 or 5 36 or 1 9 or 0..

What is the probability of getting 13 as the product when two number cubes are rolled? => 1 13 or 13 or 0 or 1..

Find the difference between the probability of getting a sum of 8 and the probability of getting a sum of 3 when two number cubes are rolled. => 1 18 or 1 12 or 1 36 or 1 9..