AI Made - Part 2 - Week 12 to 13

• What is summation?

  A sum of all terms in each pattern
• How is summation denoted?

  By the symbol Σ (sigma)
• How is the summation of x sub i from 1 to 10 expressed?

  As $\sigma_{i=1}^{10} x_i$
• What does the notation $\sigma_{i=1}^{n} f_i x_i$ expand to?


  • $f_1 x_1 +$$f_2 x_2 +$$f_3 x_3 +$$\ldots +$$f_n x_n$
• How does the notation $\sigma_{i=3}^{15} (f_i + x_i)^2$ expand?


  • $(f_3 + x_3)^2 +$$(f_4 + x_4)^2 +$$\ldots +$$(f_{15} +$$x_{15})^2$
• What does $\sigma_{i=3}^{10} x_i +$$\sigma_{i=1}^{20} y_i$ represent?


  • $(x_3 + x_4 + \ldots + x_{10}) +$$(y_1 + y_2 + \ldots + y_{20})$
• How is the summation of Q1 to Q6 expressed?

  • $\sigma_{i=1}^{6} Q_i$
• How is the summation of b5 to b9 expressed?

  • $\sigma_{i=5}^{9} b_i$
• How is the summation of (5 + A3) to (5 + A7) expressed?

  • $\sigma_{i=3}^{7} (5 + A_i)$
• What is the expanded form of $\sigma_{i=5}^{10} C_i$?


  • $C_5 +$$C_6 +$$C_7 +$$C_8 +$$C_9 +$$C_{10}$
• What is the expanded form of $\sigma_{i=3}^{7} y_i^2 +$$3$?


  • $y_3^2 +$$y_4^2 +$$y_5^2 +$$y_6^2 +$$y_7^2 +$$3$
• What is the expanded form of $\sigma_{i=1}^{5} x_i +$$y_i^3$?


  • $x_1 +$$x_2 +$$x_3 +$$x_4 +$$x_5 +$$y_1^3 +$$y_2^3 +$$y_3^3 +$$y_4^3 +$$y_5^3$
• What is the expanded form of $\sigma_{i=1}^{12} 9D_i$?


  • $9D_1 +$$9D_2 +$$\ldots +$$9D_{12}$
• What is the expanded form of $\sigma_{i=10}^{15} x_i - 3y_i^2$?


  • $x_{10} +$$x_{11} +$$x_{12} +$$x_{13} +$$x_{14} +$$x_{15} - 3(y_{10}^2 +$$y_{11}^2 +$$y_{12}^2)$
• How can you express $x_2 y_2 +$$x_3 y_3 +$$\ldots +$$x_6 y_6$ in summation notation?


  • $\sigma_{i=2}^{6} x_i y_i$
• How can you express $(c_3 d_3)^2 +$$(c_4 d_4)^2 +$$\ldots +$$(c_{20} d_{20})^2$ in summation notation?


  • $\sigma_{i=3}^{20} (c_i d_i)^2$
• How can you express $(4 - d_1)^2 +$$(4 - d_2)^2 +$$\ldots +$$(4 - d_{10})^2$ in summation notation?


  • $\sigma_{i=1}^{10} (4 - d_i)^2$
• How can you express $f_1(x_1 - y)^2 +$$f_2(x_2 - y)^2 +$$\ldots +$$f_{30}(x_{30} - y)^2$ in summation notation?


  • $\sigma_{i=1}^{30} f_i (x_i - y)^2$
• How can you express $x_1 +$$x_2 +$$\ldots +$$x_{15} - 15$ in summation notation?


  • $\sigma_{i=1}^{15} x_i - 15$
• How can you express $x_{10} +$$x_{11} +$$\ldots +$$x_{20} - y_{15} +$$y_{16} +$$\ldots +$$y_{30}$ in summation notation?


  • $\sigma_{i=10}^{20} x_i - \sigma_{j=15}^{30} y_j$
• What is the average age of boys based on the given pairs?

  Sum of boys' ages divided by 5
• What is the average age of girls based on the given pairs?

  Sum of girls' ages divided by 5