number of 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 (n+m) an..

3. To find the sum to the cubes of first n natural numbers. ..

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 approximately ..

A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is..

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 ; sub-triplicate ra..

Find the number of cubes required to make the structure shown. => 22 or 40 or 32 or 44..

Which of these bar graphs shows the correct number of cubes and triangles? => Figure 1 or Figure 2 or Figure 3..

Two number cubes are rolled simultaneously. What is the probability that the difference of the two numbers on the number cubes is 2? => 1 9 or 5 6 or 1 6 or 2 9..