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:
f(x,y) =
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)) ?
=
c(x+1)(4-x)((x+1)/6)(-2x2+5x+18) ?
=
c((x+1)2/6(4-x)(-2x2+5x+18) ?
= 12c+42c+60c+40c
= 154c
c=1/154
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