Question

Q: Assistance in understanding this exercise on how 1/154 came about for finding the value c, thanks.

**Please give the step by steps with details to completely see how the solution came about.

1) 0+1+2+...+x= x(x+1)/2 ?

    0²+1²+2²+...+x²= x(x+1)(2x+1)/6 ?

using the equations from the previous parts:

3
$sum_{y=0}^{x}$ f(x,y) =
3
$sum_{y=0}^{x}$c(x+1)(4-x)(-y²+2y+3)

                      = c(x+1)(4-x)(-x(x+1)(2x+1)/6 + 2(x(x+1)/2) + 3(x+1)) ?

3

                      = c(x+1)(4-x)((x+1)/6)(-2x²+5x+18) ?

3

                      = c((x+1)²/6(4-x)(-2x²+5x+18) ?

3

                       = 12c+42c+60c+40c

                      = 154c

                      c=1/154

Answer 1

Please see the page no​​​​​​