In class, we developed the formula
(a) Use the formula (using appropriate substitutions) to find the closed form for β2
= 2
(b) Use the formula in the notes for β
= 13 to find the closed form expression form for
β
= 3 (assume a β₯ 1 and a β€ b)
(c) In class, we developed the formula
Use this formula and some algebra to derive a closed form for the sum β
= 0( β 1)2 β 1
(d) Test your closed form solution in (c) to find the value of β3
= 0( β 1)2 β 1 and see if
it matches the manual computation of the 4 terms of the sum.