Counter
Mathematics Dictionary
Dr. K. G. Shih
Question and Answer
Questions



  • Keyword | S005 - Sequence in Pascal triangle
  • Keyword | S075 - Sequence : 1, 3, 7, 13, 21, ....
  • Keyword | S009 - Sequences : 1, 3, 7, 13, 21, ....
      * Example 1 : Find T(n) * Example 2 : Find S(n)
  • Keyword | S009 Sequences : 1, 4, 10, 20, 35, ....
      * Example 1 : Find T(n) * Example 2 : Find S(n)
  • Keyword | S007 - Sequence of numbers in cube patterns
  • Keyword | S006 - Sequence of numbers in square patterns
  • Keyword | S007 - Sequence of numbers in triangular patterns
  • Keyword | S031 - Series : Prove that Sum[1/(n*(n+1)) = 1 - 1/(n+1)
  • Keyword | S044 - Series : Prove that Sum[(n*(n+1)/2) = n*(n+1)*(n+2)/6
  • Keyword | S054 - Series : S(n) = cos(x) + cos(3*x) + ... + cos((2*n-1)*x)
  • Keyword | S055 - Series : S(n) = sin(x)^2 + sin(2*x)^2 + ... + sin(2*x)^n
  • Keyword | S004- Series : Special
    • 1. S(n) = Sum[1/(n*(n+1))]
    • 2. S(n) = Sum[1/((2*n-1)*(2*n+1))]
    • 3. S(n) = Sum[1/(n*(n+1)*(n+2))]
    • 4. S(n) = Sum[(1-1/(n^2))] where n GT 2
  • Keyword | S001 - Series : Sum[n^2] = n*(n+1)*(2*n+1)/6
    • 1. Prove by observation
    • 2. prove by using sum[C(n+1,2)] = C(n+2,3)
    • 3. Prove by induction
    • 4. Prove by Sum[(x+1)^3 - x^3] = (x + 1)^3 - 1
  • Keyword | S002 - Series : Sum[n^3] = (n*(n+1)/2)^2
    • 1. Prove by observation
    • 2. prove by using sum[C(n+2,3)] = C(n+3,4)
    • 3. Prove by induction
    • 4. Prove by Sum[(x+1)^4 - x^4] = (x + 1)^4 - 1
  • Keyword | S003 - Series : Sum[n^4] = (n*(6*n^4 + 15*n^3 + 10*n^2 - 1)/30
  • Keyword | S067 - sin(1) + sin(2) + sin(3) + ...... + sin(359) + sin(360)
  • Keyword | F322 - sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B)
    • 1. Find sin(15) without calculator
    • 2. Find sin(75) without calculator
  • Keyword | S061 - sin(x + y) LT (sin(x) + sin(y)), If x,y are acute angle
  • Keyword | S062 - sin(x + y) = (sin(x) + sin(y)), find the conditions
  • Keyword | S064 - sin(1*pi/16)^4 +sin(3*pi/16)^4 +sin(5*pi/16)^4 +sin(7*pi/16)^4 = ?
  • Keyword | S021 - Slope and area of triangle : Coordinate Geometry
  • Keyword | S082 - Square ABCD inscribed unit circle
    • Prove that PA^2 + PB^2 + PC^2 + PD^2 = 2*4
  • Keyword | S006 - Squares in squares patterns
  • Keyword | S107 - Square : Inscribed an equilateral triangle
  • Keyword | S057 - Sum to product
    • sin(A) + sin(B) = p and cos(A) + cos(B) = q, find sin(A+B)
  • Keyword | F010 - Symmetrical matrix order 5
    • 1. Find element row 1 and column 5 for power 3 of the matrix
    • 2. Find element row 1 and column 5 for power 4 of the matrix
    • 3. Find element row 1 and column 5 for power 5 of the matrix


    Go to Begin
    • Show Room of MD2002 Contact Dr. Shih Math Examples Room
    Copyright © Dr. K. G. Shih, Nova Scotia, Canada.
    1