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In-center theory
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Induction method
- AL 14 02 Sum[n*(n+1)/2] = n*(n+1)*(n+2)/6
- AL 14 03 Sum[n^2] = n*(n+1)*(2*n+1)/6
- AL 14 04 Sum[n^3] = ((n*(n+1))/2)^2
- AL 14 05 1/(1*2) + 1/(2*3) + ..... + 1/(n*(n+1)) = 1 - 1/(n+1)
- AL 14 06 Sum[1/((2*n-1)*(2*n+1)) = (1 - 1/(2*n+1))/2
- AL 14 07 Sum[1/(n*(n+1)*(n+2)] = n*(n+3)/(4*(n+1)*(n+2)
- AL 14 08 Sum[(2*n-1)^2] = n*(4*n^2 - 1)/3
- AL 14 09 Sum[n*((n+1)^2)] = n*(n+1)*(n+2)*(3*n+5)/12
- AL 14 10 S(n) = (1 -4/1)*(1 - 4/9)*(1 - 4/25)*(1 - 4/49)*......
- AL 14 11 S(n) = (1 + 1)*(1 + 1/2)*(1 + 1/3)*.....*(1 + 1/n) = n + 1
- AL 14 12 S(n) = (1^2)/(1*3) + (2^2)/(3*5) + (3^2)/(5*7) + .... = (n*(n+1))/(2*(2*n+1))
- AL 14 13 Is this series S(n) = 2 + 4 + 6 + ..... + 2*n = (n + 1/2)^2 true ?
- AL 14 14 Is S(n) = n^2 + n + 41 always a prime number ?
- AL 14 15 Prove that ((n^3) + 3*(n^2) + n)/3 is an integer
- AL 14 16 Prove that (2*(n^3) + 3*(n^2) + n) is divisible by 6
- AL 14 17 Prove that 1! + 2! + 3! + 4! + ..... + n! = 3^(n-1)
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Integral Table
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Internation flag codes of numbers and english characters
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Intersection of quadratic function with y = 1/x
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Intersection of quadratic function with y = a*x + b
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Intersection of quadratic function with its inverse
- 1. Find intersections of y = x^2 - 2*x + 4 with its inverse
- 2. Find intersections of y = x^2 - 3*x + 4 with its inverse
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Intersection of quadratic function with its inverse
- 1. How many intersections of quadratic function with its inverse ?
- 2. Find intersections of y = x^2 - 5*x + 8 with its inverse
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Intersection of quadratic function with its inverse
- 1. (b - 1)^2 - 4*a*c = 0 has one point of intersection
- 2. Find intersections of y = x^2 - 6*x + 8 with its inverse
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Inverse : Intersections of y = x^2 - 6*x + 8 and its inverse
- 1. It has four points of intersection
- 2. Find point of intersections of y = x^2 - 5*x + 8 with its inverse
- 3. Find point of intersections of y = x^2 - 2*x + 4 with its inverse
- 4. Find point of intersections of y = x^2 - 3*x + 4 with its inverse
- 5.
Sketch
Inverse of y = a*x^2 + b*x + c
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Inverse hyperbolic functions : Formula and example
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Inverse : Intersection of linear function with its inverse
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Inverse : Intersection of quadratic function with its inverse
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