#1 In class, we developed the formula =1 12 = 12 =0 = 2n+3n+n (a)...

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#1 In class, we developed the formula Σ=1 12 = Στο 12 =0 = 2n³+3n²+n (a) Use the formula (using appropriate substitutions) to find the closed form for Σ²2n i² i=1 (b) Use the formula in the notes for -₁ 1³ to find the closed form expression form for Ei ai³ (assume a ≥ 1 and a ≤ b) (c) In class, we developed the formula k Σi2¹. (k-1)2k+¹ +2 i=1 Use this formula and some algebra to derive a closed form for the sum _o(i – 1)2i–1 (d) Test your closed form solution in (c) to find the value of Σ²-o(i − 1)2i-¹ and see if it matches the manual computation of the 4 terms of the sum. #1 In class, we developed the formula Σ=1 12 = Στο 12 =0 = 2n³+3n²+n (a) Use the formula (using appropriate substitutions) to find the closed form for Σ²2n i² i=1 (b) Use the formula in the notes for -₁ 1³ to find the closed form expression form for Ei ai³ (assume a ≥ 1 and a ≤ b) (c) In class, we developed the formula k Σi2¹. (k-1)2k+¹ +2 i=1 Use this formula and some algebra to derive a closed form for the sum _o(i – 1)2i–1 (d) Test your closed form solution in (c) to find the value of Σ²-o(i − 1)2i-¹ and see if it matches the manual computation of the 4 terms of the sum.

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Step1 To find the closed form for n in i 2 we can use the formula n in i 2 2n 3 3n 2 n6 We need to ... View the full answer