Arithmetic Geometric
Arithmetic Geometric Series - A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..
Arithmetic Geometric Series - A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..Question 10
Question: Find n if P(n,4) = 20P(n,2) Answer: ..
Question: Find n if P(n,4) = 20P(n,2) Answer: ..Question 3
Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..
Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..Question 1
Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we get ..
Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we get ..Suggested answer:
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 1 = 6, A 2 2 = -2, A 2 3 = -14 A 3 1 = 1, A 3 2 = 5, A 3 3 = 3 ..
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 1 = 6, A 2 2 = -2, A 2 3 = -14 A 3 1 = 1, A 3 2 = 5, A 3 3 = 3 ..Verification by numerical problems
\ A + B = B + A \ A + B = B ..
\ A + B = B + A \ A + B = 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..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 ..See what our Users say :
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