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Verification by numerical problems
then show that (A+B)+C = A+(B..
then show that (A+B)+C = A+(B..Suggested answer:
We have 3A - 2B = 3A+(-2)..
We have 3A - 2B = 3A+(-2)..Example:
The matrices are scalar matrices of order 2 and 3 respectivel..
The matrices are scalar matrices of order 2 and 3 respectivel..Suggested answer:
We are to select 4 students from 32. This selection can done i..
We are to select 4 students from 32. This selection can done i..Proof:
If r = s, there is nothing to prove. Now, If r < s, then n - r > n - s, then the above equation becomes Since both sides are products of (s-r), consecutive integers in Similarly it can be proved that n = r + s if r > s...
If r = s, there is nothing to prove. Now, If r < s, then n - r > n - s, then the above equation becomes Since both sides are products of (s-r), consecutive integers in Similarly it can be proved that n = r + s if r > s...Examples:
8! = 8 x 7 x 6 x 5 x4 x 3 x 2 x 1 = 40320 ..
8! = 8 x 7 x 6 x 5 x4 x 3 x 2 x 1 = 40320 ..Corollary 1:
If we put r = n in the above formula, the..
If we put r = n in the above formula, the..General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..Examples:
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..To insert n Harmonic Means between two given quantities
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 b. Let d = common difference of the A.P. Hence h 1 , h..
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 b. Let d = common difference of the A.P. Hence h 1 , h..See what our Users say :
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